Information on Result #547875

There is no linear OA(4139, 163, F4, 102) (dual of [163, 24, 103]-code), because construction Y1 would yield
  1. OA(4138, 149, S4, 102), but
    • the linear programming bound shows that M ≥ 11 769278 720446 703333 267659 747956 551886 187319 922656 933070 157940 129170 842786 675855 465333 653504 / 85 907459 > 4138 [i]
  2. OA(424, 163, S4, 14), but

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 OA(4140, 164, F4, 103) (dual of [164, 24, 104]-code) [i]Truncation
2No linear OOA(4140, 163, F4, 2, 103) (dual of [(163, 2), 186, 104]-NRT-code) [i]m-Reduction for OOAs
3No linear OOA(4142, 163, F4, 2, 105) (dual of [(163, 2), 184, 106]-NRT-code) [i]
4No linear OOA(4143, 163, F4, 2, 106) (dual of [(163, 2), 183, 107]-NRT-code) [i]
5No linear OOA(4144, 163, F4, 2, 107) (dual of [(163, 2), 182, 108]-NRT-code) [i]
6No linear OOA(4145, 163, F4, 2, 108) (dual of [(163, 2), 181, 109]-NRT-code) [i]
7No linear OOA(4146, 163, F4, 2, 109) (dual of [(163, 2), 180, 110]-NRT-code) [i]
8No linear OOA(4147, 163, F4, 2, 110) (dual of [(163, 2), 179, 111]-NRT-code) [i]
9No linear OOA(4148, 163, F4, 2, 111) (dual of [(163, 2), 178, 112]-NRT-code) [i]
10No linear OOA(4139, 163, F4, 2, 102) (dual of [(163, 2), 187, 103]-NRT-code) [i]Depth Reduction
11No linear OOA(4139, 163, F4, 3, 102) (dual of [(163, 3), 350, 103]-NRT-code) [i]
12No digital (37, 139, 163)-net over F4 [i]Extracting Embedded Orthogonal Array
13No linear OA(4140, 204, F4, 102) (dual of [204, 64, 103]-code) [i]Construction Y1 (Bound)