Information on Result #1734274
Digital (31, 46, 1057)-net over F16, using net defined by OOA based on linear OOA(1646, 1057, F16, 18, 15) (dual of [(1057, 18), 18980, 16]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1646, 4229, F16, 2, 15) (dual of [(4229, 2), 8412, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1646, 4230, F16, 2, 15) (dual of [(4230, 2), 8414, 16]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1646, 4230, F16, 15) (dual of [4230, 4184, 16]-code), using
- 128 step Varšamov–Edel lengthening with (ri) = (2, 13 times 0, 1, 113 times 0) [i] based on linear OA(1643, 4099, F16, 15) (dual of [4099, 4056, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(1643, 4096, F16, 15) (dual of [4096, 4053, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- 128 step Varšamov–Edel lengthening with (ri) = (2, 13 times 0, 1, 113 times 0) [i] based on linear OA(1643, 4099, F16, 15) (dual of [4099, 4056, 16]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1646, 4230, F16, 15) (dual of [4230, 4184, 16]-code), using
- discarding factors / shortening the dual code based on linear OOA(1646, 4230, F16, 2, 15) (dual of [(4230, 2), 8414, 16]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.