Best Known (86, 105, s)-Nets in Base 4
(86, 105, 1823)-Net over F4 — Constructive and digital
Digital (86, 105, 1823)-net over F4, using
- 41 times duplication [i] based on digital (85, 104, 1823)-net over F4, using
- net defined by OOA [i] based on linear OOA(4104, 1823, F4, 19, 19) (dual of [(1823, 19), 34533, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4104, 16408, F4, 19) (dual of [16408, 16304, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4104, 16410, F4, 19) (dual of [16410, 16306, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(18) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4104, 16410, F4, 19) (dual of [16410, 16306, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4104, 16408, F4, 19) (dual of [16408, 16304, 20]-code), using
- net defined by OOA [i] based on linear OOA(4104, 1823, F4, 19, 19) (dual of [(1823, 19), 34533, 20]-NRT-code), using
(86, 105, 11522)-Net over F4 — Digital
Digital (86, 105, 11522)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4105, 11522, F4, 19) (dual of [11522, 11417, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4105, 16412, F4, 19) (dual of [16412, 16307, 20]-code), using
- construction XX applied to Ce(18) ⊂ Ce(14) ⊂ Ce(13) [i] based on
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(471, 16384, F4, 14) (dual of [16384, 16313, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(18) ⊂ Ce(14) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4105, 16412, F4, 19) (dual of [16412, 16307, 20]-code), using
(86, 105, large)-Net in Base 4 — Upper bound on s
There is no (86, 105, large)-net in base 4, because
- 17 times m-reduction [i] would yield (86, 88, large)-net in base 4, but