Best Known (146−27, 146, s)-Nets in Base 4
(146−27, 146, 1262)-Net over F4 — Constructive and digital
Digital (119, 146, 1262)-net over F4, using
- net defined by OOA [i] based on linear OOA(4146, 1262, F4, 27, 27) (dual of [(1262, 27), 33928, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4146, 16407, F4, 27) (dual of [16407, 16261, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4146, 16410, F4, 27) (dual of [16410, 16264, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4146, 16410, F4, 27) (dual of [16410, 16264, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4146, 16407, F4, 27) (dual of [16407, 16261, 28]-code), using
(146−27, 146, 10511)-Net over F4 — Digital
Digital (119, 146, 10511)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4146, 10511, F4, 27) (dual of [10511, 10365, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4146, 16410, F4, 27) (dual of [16410, 16264, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4146, 16410, F4, 27) (dual of [16410, 16264, 28]-code), using
(146−27, 146, large)-Net in Base 4 — Upper bound on s
There is no (119, 146, large)-net in base 4, because
- 25 times m-reduction [i] would yield (119, 121, large)-net in base 4, but