Details for entry \(A_2(12,4;5)\)

Lower bounds

• ef_computation ( show
  [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 3, 5, 7), (0, 2, 4, 5, 7), (0, 1, 3, 6, 8), (0, 2, 3, 6, 7), (2, 3, 4, 5, 6), (1, 2, 3, 5, 8), (0, 1, 2, 7, 8), (0, 1, 4, 6, 7), (0, 1, 4, 5, 8), (0, 2, 3, 5, 9), (1, 2, 3, 6, 9), (1, 2, 4, 6, 8), (1, 3, 4, 5, 9), (1, 2, 4, 5, 10), (0, 2, 4, 6, 9), (0, 1, 2, 9, 10), (1, 2, 3, 7, 10), (1, 3, 4, 7, 8), (1, 2, 4, 7, 9), (0, 3, 4, 5, 10), (1, 3, 4, 6, 10), (0, 3, 4, 7, 9), (0, 2, 3, 8, 10), (0, 3, 4, 6, 11), (0, 1, 3, 9, 11), (2, 3, 4, 8, 9), (1, 3, 5, 6, 11), (2, 3, 4, 7, 11), (1, 2, 5, 7, 11), (0, 2, 4, 8, 11), (2, 5, 6, 7, 8), (0, 1, 4, 10, 11), (2, 4, 6, 7, 10), (0, 3, 5, 8, 11), (1, 5, 6, 7, 9), (0, 4, 6, 8, 10), (2, 3, 6, 8, 11), (0, 3, 6, 9, 10), (0, 2, 5, 10, 11), (0, 5, 6, 8, 9), (0, 2, 7, 9, 11), (1, 2, 6, 10, 11), (3, 5, 6, 7, 10), (0, 5, 6, 7, 11), (1, 5, 6, 8, 10), (0, 4, 5, 9, 11), (1, 3, 8, 9, 10), (1, 4, 6, 9, 11), (1, 2, 8, 9, 11), (0, 5, 7, 8, 10), (3, 5, 7, 8, 9), (2, 5, 7, 9, 10), (2, 5, 6, 9, 11), (4, 5, 6, 8, 11), (0, 3, 7, 10, 11), (4, 5, 6, 9, 10), (4, 6, 7, 8, 9), (1, 6, 7, 8, 11), (4, 5, 7, 10, 11), (2, 6, 8, 9, 10), (3, 6, 7, 9, 11), (3, 4, 8, 10, 11), (2, 3, 9, 10, 11), (1, 5, 9, 10, 11), (2, 7, 8, 10, 11), (0, 8, 9, 10, 11)]
  ) : 299769965
• greedy_multicomponent ( show
  q^28 + q^24 + q^22 + 8*q^20 + q^19 + q^18 + 3*q^17 + 2*q^16 + 3*q^15 + 4*q^14 + 2*q^13 + 5*q^12 + q^11 + 2*q^10 + 2*q^9 + 2*q^8 + 2*q^7 + 5*q^6 + 4*q^4 + q^3 + q^2 + q + 1
  ) : 299313295
• LiuChangFeng2019_Theo_3_16 ( ) : 297813023
• JohnsonLB ( ) : 296675704
• LiuChangFeng2019_Theo_3_12 ( ) : 288682504
• construction_ST_B_recursive ( ) : 287445033
• construction_ST_B ( ) : 287221351
• LiuChangFeng2019_Theo_3_14 ( ) : 287211520
• two_pivot_block_construction ( ) : 286326784
• CKMP2019_Cor_45 ( show
  (7,),(3,),(2,)
  ) : 273771016
• CKMP2019_Cor_42 ( (5, 7) ) : 273754632
• CKMP2019_Lem_41 ( (5, 7) ) : 273754632
• generalized_linkage ( 5,0 ) : 273754632
• generalized_linkage_multipleblocks ( show
  [5, 7],[0, 0]
  ) : 273754632
• LiuChangFeng2019_Theo_2_6 ( ) : 270856712
• improved_linkage ( 5 ) : 269614280
• multicomponent ( ) : 269485057
• linkage_GLT ( 5 ) : 268435497
• LMRD ( ) : 268435456
• HKK_lemma_2_4_lower_bound ( ) : 39353594
• ChenHeWengXu2019_T31 ( ) : 38873567
• graham_sloane ( ) : 27943597
• sphere_covering ( ) : 14530671
• coset_construction_parallelism_part ( show
  [(46872, '(1,4), 6: 46872'), (1499904, '(1,4), 6: 1499904')]
  ) : 1499904
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 11, o ) : 445207739
• ilp_1 ( 1 ) : 445207739
• improved_johnson ( ) : 445207739
• johnson_1 ( ) : 445207739
• anticode ( ) : 448741293
• ilp_2 ( 4 ) : 448741293
• linear_programming_bound ( ) : 448741293
• singleton ( ) : 866251507
• ilp_4 ( 11 ) : 901015982
• johnson_2 ( ) : 901015982
• HKK_lemma_2_4_upper_bound ( ) : 908166902
• ilp_3 ( 6 ) : 1816333805
• all_subs ( ) : 114429029715
• sphere_packing ( ) : 114429029715

Bound for codes containing the lifted MRD code

Do you have better bounds?