Best Known (203−26, 203, s)-Nets in Base 3
(203−26, 203, 13635)-Net over F3 — Constructive and digital
Digital (177, 203, 13635)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 15, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-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 (2, 15, 8)-net over F3, using
(203−26, 203, 69649)-Net over F3 — Digital
Digital (177, 203, 69649)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3203, 69649, F3, 2, 26) (dual of [(69649, 2), 139095, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3203, 88608, F3, 2, 26) (dual of [(88608, 2), 177013, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3203, 177216, F3, 26) (dual of [177216, 177013, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3203, 177217, F3, 26) (dual of [177217, 177014, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [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(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(315, 70, F3, 6) (dual of [70, 55, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3203, 177217, F3, 26) (dual of [177217, 177014, 27]-code), using
- OOA 2-folding [i] based on linear OA(3203, 177216, F3, 26) (dual of [177216, 177013, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(3203, 88608, F3, 2, 26) (dual of [(88608, 2), 177013, 27]-NRT-code), using
(203−26, 203, large)-Net in Base 3 — Upper bound on s
There is no (177, 203, large)-net in base 3, because
- 24 times m-reduction [i] would yield (177, 179, large)-net in base 3, but