Information on Result #547706

There is no linear OA(2205, 363, F2, 88) (dual of [363, 158, 89]-code), because construction Y1 would yield
  1. OA(2204, 299, S2, 88), but
    • adding a parity check bit [i] would yield OA(2205, 300, S2, 89), but
      • the linear programming bound shows that M ≥ 416927 463188 475542 795463 940731 898983 181308 104641 213119 598295 609827 594303 154474 074874 094714 331435 368448 / 5584 401256 756961 297780 513782 298869 514125 > 2205 [i]
  2. linear OA(2158, 363, F2, 64) (dual of [363, 205, 65]-code), but
    • the improved Johnson bound shows that N ≤ 1214 271568 452769 866939 025066 626311 211727 927188 642255 823141 634304 < 2205 [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OA(2206, 364, F2, 89) (dual of [364, 158, 90]-code) [i]Truncation
2No linear OOA(2206, 363, F2, 2, 89) (dual of [(363, 2), 520, 90]-NRT-code) [i]m-Reduction for OOAs
3No linear OOA(2205, 363, F2, 2, 88) (dual of [(363, 2), 521, 89]-NRT-code) [i]Depth Reduction
4No linear OOA(2205, 363, F2, 3, 88) (dual of [(363, 3), 884, 89]-NRT-code) [i]
5No linear OOA(2205, 363, F2, 4, 88) (dual of [(363, 4), 1247, 89]-NRT-code) [i]
6No linear OOA(2205, 363, F2, 5, 88) (dual of [(363, 5), 1610, 89]-NRT-code) [i]
7No linear OOA(2205, 363, F2, 6, 88) (dual of [(363, 6), 1973, 89]-NRT-code) [i]
8No linear OOA(2205, 363, F2, 7, 88) (dual of [(363, 7), 2336, 89]-NRT-code) [i]
9No linear OOA(2205, 363, F2, 8, 88) (dual of [(363, 8), 2699, 89]-NRT-code) [i]
10No digital (117, 205, 363)-net over F2 [i]Extracting Embedded Orthogonal Array