Best Known (190, 209, s)-Nets in Base 3
(190, 209, 932150)-Net over F3 — Constructive and digital
Digital (190, 209, 932150)-net over F3, using
- 31 times duplication [i] based on digital (189, 208, 932150)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (18, 27, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 9, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 9, 28)-net over F27, using
- digital (162, 181, 932066)-net over F3, using
- net defined by OOA [i] based on linear OOA(3181, 932066, F3, 19, 19) (dual of [(932066, 19), 17709073, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3181, 8388595, F3, 19) (dual of [8388595, 8388414, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3181, 8388595, F3, 19) (dual of [8388595, 8388414, 20]-code), using
- net defined by OOA [i] based on linear OOA(3181, 932066, F3, 19, 19) (dual of [(932066, 19), 17709073, 20]-NRT-code), using
- digital (18, 27, 84)-net over F3, using
- (u, u+v)-construction [i] based on
(190, 209, 4194413)-Net over F3 — Digital
Digital (190, 209, 4194413)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3209, 4194413, F3, 2, 19) (dual of [(4194413, 2), 8388617, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(328, 112, F3, 2, 9) (dual of [(112, 2), 196, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(328, 112, F3, 9) (dual of [112, 84, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(328, 125, F3, 9) (dual of [125, 97, 10]-code), using
- a “BZ†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(328, 125, F3, 9) (dual of [125, 97, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(328, 112, F3, 9) (dual of [112, 84, 10]-code), using
- linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- linear OOA(328, 112, F3, 2, 9) (dual of [(112, 2), 196, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(190, 209, large)-Net in Base 3 — Upper bound on s
There is no (190, 209, large)-net in base 3, because
- 17 times m-reduction [i] would yield (190, 192, large)-net in base 3, but