Best Known (26, 26+8, s)-Nets in Base 3
(26, 26+8, 328)-Net over F3 — Constructive and digital
Digital (26, 34, 328)-net over F3, using
- 32 times duplication [i] based on digital (24, 32, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 8, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 8, 82)-net over F81, using
(26, 26+8, 625)-Net over F3 — Digital
Digital (26, 34, 625)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(334, 625, F3, 8) (dual of [625, 591, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(334, 742, F3, 8) (dual of [742, 708, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(331, 729, F3, 8) (dual of [729, 698, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(319, 729, F3, 5) (dual of [729, 710, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(334, 742, F3, 8) (dual of [742, 708, 9]-code), using
(26, 26+8, 12572)-Net in Base 3 — Upper bound on s
There is no (26, 34, 12573)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 16678 149607 553809 > 334 [i]