Information on Result #548071

There is no linear OA(4107, 231, F4, 75) (dual of [231, 124, 76]-code), because construction Y1 would yield
  1. OA(4106, 143, S4, 75), but
    • the linear programming bound shows that M ≥ 189 312298 968815 860250 485793 283965 413843 284713 743252 821000 560707 597443 674955 116200 018233 524224 / 27631 043169 340831 430975 152245 > 4106 [i]
  2. linear OA(4124, 231, F4, 88) (dual of [231, 107, 89]-code), but
    • discarding factors / shortening the dual code would yield linear OA(4124, 210, F4, 88) (dual of [210, 86, 89]-code), but
      • construction Y1 [i] would yield
        1. OA(4123, 150, S4, 88), but
          • the linear programming bound shows that M ≥ 22915 666113 439092 609099 444232 414491 754857 959622 104295 992957 494311 648680 329878 580928 609806 974976 / 136 168406 561048 662801 > 4123 [i]
        2. OA(486, 210, S4, 60), but
          • discarding factors would yield OA(486, 145, S4, 60), but
            • the linear programming bound shows that M ≥ 70 960269 863126 606518 991667 215730 563206 075021 389069 425781 018295 735734 868068 159984 954116 355960 140231 669388 460318 751919 101866 886859 928826 023614 873600 / 11532 795767 709720 554647 969916 716816 544438 820799 421172 775769 384715 477815 805045 795696 528849 736837 > 486 [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OOA(4107, 231, F4, 2, 75) (dual of [(231, 2), 355, 76]-NRT-code) [i]Depth Reduction
2No linear OOA(4107, 231, F4, 3, 75) (dual of [(231, 3), 586, 76]-NRT-code) [i]