Best Known (169, 199, s)-Nets in Base 3
(169, 199, 1484)-Net over F3 — Constructive and digital
Digital (169, 199, 1484)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (154, 184, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 46, 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, 46, 370)-net over F81, using
- digital (0, 15, 4)-net over F3, using
(169, 199, 13336)-Net over F3 — Digital
Digital (169, 199, 13336)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3199, 13336, F3, 30) (dual of [13336, 13137, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3199, 19755, F3, 30) (dual of [19755, 19556, 31]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3197, 19753, F3, 30) (dual of [19753, 19556, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(21) [i] based on
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(316, 70, F3, 7) (dual of [70, 54, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(30) ⊂ Ce(21) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3197, 19753, F3, 30) (dual of [19753, 19556, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3199, 19755, F3, 30) (dual of [19755, 19556, 31]-code), using
(169, 199, 6863480)-Net in Base 3 — Upper bound on s
There is no (169, 199, 6863481)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 88538 186653 147404 948342 359792 513362 706090 631762 507776 879817 435443 877945 075700 832618 204419 964491 > 3199 [i]