Best Known (145, 159, s)-Nets in Base 3
(145, 159, 1198455)-Net over F3 — Constructive and digital
Digital (145, 159, 1198455)-net over F3, using
- 32 times duplication [i] based on digital (143, 157, 1198455)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (14, 21, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 7, 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, 7, 28)-net over F27, using
- digital (122, 136, 1198371)-net over F3, using
- net defined by OOA [i] based on linear OOA(3136, 1198371, F3, 14, 14) (dual of [(1198371, 14), 16777058, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3136, 8388597, F3, 14) (dual of [8388597, 8388461, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3136, 8388597, F3, 14) (dual of [8388597, 8388461, 15]-code), using
- net defined by OOA [i] based on linear OOA(3136, 1198371, F3, 14, 14) (dual of [(1198371, 14), 16777058, 15]-NRT-code), using
- digital (14, 21, 84)-net over F3, using
- (u, u+v)-construction [i] based on
(145, 159, 5063222)-Net over F3 — Digital
Digital (145, 159, 5063222)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3159, 5063222, F3, 14) (dual of [5063222, 5063063, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3159, large, F3, 14) (dual of [large, large−159, 15]-code), using
- 23 times code embedding in larger space [i] based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 23 times code embedding in larger space [i] based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3159, large, F3, 14) (dual of [large, large−159, 15]-code), using
(145, 159, large)-Net in Base 3 — Upper bound on s
There is no (145, 159, large)-net in base 3, because
- 12 times m-reduction [i] would yield (145, 147, large)-net in base 3, but