Best Known (195, 241, s)-Nets in Base 3
(195, 241, 896)-Net over F3 — Constructive and digital
Digital (195, 241, 896)-net over F3, using
- 31 times duplication [i] based on digital (194, 240, 896)-net over F3, using
- t-expansion [i] based on digital (193, 240, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 60, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 60, 224)-net over F81, using
- t-expansion [i] based on digital (193, 240, 896)-net over F3, using
(195, 241, 3413)-Net over F3 — Digital
Digital (195, 241, 3413)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3241, 3413, F3, 46) (dual of [3413, 3172, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 6561, F3, 46) (dual of [6561, 6320, 47]-code), using
- an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- discarding factors / shortening the dual code based on linear OA(3241, 6561, F3, 46) (dual of [6561, 6320, 47]-code), using
(195, 241, 470767)-Net in Base 3 — Upper bound on s
There is no (195, 241, 470768)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9 687960 257035 131090 293421 225232 226491 723656 002159 662640 108738 733194 502843 918896 158428 226319 547338 742502 051641 518913 > 3241 [i]