Best Known (194−34, 194, s)-Nets in Base 3
(194−34, 194, 896)-Net over F3 — Constructive and digital
Digital (160, 194, 896)-net over F3, using
- 2 times m-reduction [i] based on digital (160, 196, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 49, 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, 49, 224)-net over F81, using
(194−34, 194, 4794)-Net over F3 — Digital
Digital (160, 194, 4794)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3194, 4794, F3, 34) (dual of [4794, 4600, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3194, 6579, F3, 34) (dual of [6579, 6385, 35]-code), using
- (u, u+v)-construction [i] based on
- linear OA(317, 18, F3, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,3)), using
- dual of repetition code with length 18 [i]
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(317, 18, F3, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,3)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(3194, 6579, F3, 34) (dual of [6579, 6385, 35]-code), using
(194−34, 194, 999317)-Net in Base 3 — Upper bound on s
There is no (160, 194, 999318)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 364 356384 566709 171731 451489 395674 223432 686279 565237 220652 099720 863052 992493 199036 873308 957965 > 3194 [i]