Best Known (246−38, 246, s)-Nets in Base 4
(246−38, 246, 3459)-Net over F4 — Constructive and digital
Digital (208, 246, 3459)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 21, 10)-net over F4, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- digital (187, 225, 3449)-net over F4, using
- net defined by OOA [i] based on linear OOA(4225, 3449, F4, 38, 38) (dual of [(3449, 38), 130837, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(4225, 65531, F4, 38) (dual of [65531, 65306, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- discarding factors / shortening the dual code based on linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(4225, 65531, F4, 38) (dual of [65531, 65306, 39]-code), using
- net defined by OOA [i] based on linear OOA(4225, 3449, F4, 38, 38) (dual of [(3449, 38), 130837, 39]-NRT-code), using
- digital (2, 21, 10)-net over F4, using
(246−38, 246, 59533)-Net over F4 — Digital
Digital (208, 246, 59533)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4246, 59533, F4, 38) (dual of [59533, 59287, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4246, 65613, F4, 38) (dual of [65613, 65367, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(28) [i] based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(421, 77, F4, 8) (dual of [77, 56, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 84, F4, 8) (dual of [84, 63, 9]-code), using
- construction X applied to Ce(37) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4246, 65613, F4, 38) (dual of [65613, 65367, 39]-code), using
(246−38, 246, large)-Net in Base 4 — Upper bound on s
There is no (208, 246, large)-net in base 4, because
- 36 times m-reduction [i] would yield (208, 210, large)-net in base 4, but