Best Known (208−38, 208, s)-Nets in Base 3
(208−38, 208, 896)-Net over F3 — Constructive and digital
Digital (170, 208, 896)-net over F3, using
- t-expansion [i] based on digital (169, 208, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 52, 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, 52, 224)-net over F81, using
(208−38, 208, 3921)-Net over F3 — Digital
Digital (170, 208, 3921)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3208, 3921, F3, 38) (dual of [3921, 3713, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 6592, F3, 38) (dual of [6592, 6384, 39]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3207, 6591, F3, 38) (dual of [6591, 6384, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3207, 6591, F3, 38) (dual of [6591, 6384, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 6592, F3, 38) (dual of [6592, 6384, 39]-code), using
(208−38, 208, 662819)-Net in Base 3 — Upper bound on s
There is no (170, 208, 662820)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1742 697806 691931 017538 292134 989719 529133 071144 498449 531518 456895 149608 226073 974450 988782 685674 807345 > 3208 [i]