Best Known (210, 250, s)-Nets in Base 3
(210, 250, 1494)-Net over F3 — Constructive and digital
Digital (210, 250, 1494)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 26, 14)-net over F3, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- digital (184, 224, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 56, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 56, 370)-net over F81, using
- digital (6, 26, 14)-net over F3, using
(210, 250, 10014)-Net over F3 — Digital
Digital (210, 250, 10014)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3250, 10014, F3, 40) (dual of [10014, 9764, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3250, 19734, F3, 40) (dual of [19734, 19484, 41]-code), using
- 4 times code embedding in larger space [i] based on linear OA(3246, 19730, F3, 40) (dual of [19730, 19484, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(33) [i] based on
- linear OA(3235, 19683, F3, 40) (dual of [19683, 19448, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(311, 47, F3, 5) (dual of [47, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(39) ⊂ Ce(33) [i] based on
- 4 times code embedding in larger space [i] based on linear OA(3246, 19730, F3, 40) (dual of [19730, 19484, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3250, 19734, F3, 40) (dual of [19734, 19484, 41]-code), using
(210, 250, 3821991)-Net in Base 3 — Upper bound on s
There is no (210, 250, 3821992)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 190684 365298 930865 802849 541091 254239 912253 284683 438903 681885 087866 142956 583092 790875 885457 792732 361101 104744 494465 645633 > 3250 [i]