Best Known (250−15, 250, s)-Nets in Base 3
(250−15, 250, 4793568)-Net over F3 — Constructive and digital
Digital (235, 250, 4793568)-net over F3, using
- 31 times duplication [i] based on digital (234, 249, 4793568)-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 (213, 228, 4793484)-net over F3, using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8157, 1198371, F81, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8157, 8388598, F81, 15) (dual of [8388598, 8388541, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8157, 8388598, F81, 15) (dual of [8388598, 8388541, 16]-code), using
- net defined by OOA [i] based on linear OOA(8157, 1198371, F81, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F81, using
- digital (14, 21, 84)-net over F3, using
- (u, u+v)-construction [i] based on
(250−15, 250, large)-Net over F3 — Digital
Digital (235, 250, large)-net over F3, using
- 39 times duplication [i] based on digital (226, 241, large)-net over F3, using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
(250−15, 250, large)-Net in Base 3 — Upper bound on s
There is no (235, 250, large)-net in base 3, because
- 13 times m-reduction [i] would yield (235, 237, large)-net in base 3, but