Best Known (202−26, 202, s)-Nets in Base 3
(202−26, 202, 13634)-Net over F3 — Constructive and digital
Digital (176, 202, 13634)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (162, 188, 13627)-net over F3, using
- net defined by OOA [i] based on linear OOA(3188, 13627, F3, 26, 26) (dual of [(13627, 26), 354114, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3188, 177151, F3, 26) (dual of [177151, 176963, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3188, 177158, F3, 26) (dual of [177158, 176970, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3188, 177158, F3, 26) (dual of [177158, 176970, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3188, 177151, F3, 26) (dual of [177151, 176963, 27]-code), using
- net defined by OOA [i] based on linear OOA(3188, 13627, F3, 26, 26) (dual of [(13627, 26), 354114, 27]-NRT-code), using
- digital (1, 14, 7)-net over F3, using
(202−26, 202, 66399)-Net over F3 — Digital
Digital (176, 202, 66399)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3202, 66399, F3, 2, 26) (dual of [(66399, 2), 132596, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3202, 88602, F3, 2, 26) (dual of [(88602, 2), 177002, 27]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3201, 88602, F3, 2, 26) (dual of [(88602, 2), 177003, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3199, 88601, F3, 2, 26) (dual of [(88601, 2), 177003, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3199, 177202, F3, 26) (dual of [177202, 177003, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3144, 177147, F3, 20) (dual of [177147, 177003, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(311, 55, F3, 5) (dual of [55, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(3199, 177202, F3, 26) (dual of [177202, 177003, 27]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3199, 88601, F3, 2, 26) (dual of [(88601, 2), 177003, 27]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3201, 88602, F3, 2, 26) (dual of [(88602, 2), 177003, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3202, 88602, F3, 2, 26) (dual of [(88602, 2), 177002, 27]-NRT-code), using
(202−26, 202, large)-Net in Base 3 — Upper bound on s
There is no (176, 202, large)-net in base 3, because
- 24 times m-reduction [i] would yield (176, 178, large)-net in base 3, but