Best Known (88−22, 88, s)-Nets in Base 3
(88−22, 88, 328)-Net over F3 — Constructive and digital
Digital (66, 88, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 22, 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
(88−22, 88, 477)-Net over F3 — Digital
Digital (66, 88, 477)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(388, 477, F3, 22) (dual of [477, 389, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(388, 742, F3, 22) (dual of [742, 654, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(385, 729, F3, 22) (dual of [729, 644, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(373, 729, F3, 19) (dual of [729, 656, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(388, 742, F3, 22) (dual of [742, 654, 23]-code), using
(88−22, 88, 16094)-Net in Base 3 — Upper bound on s
There is no (66, 88, 16095)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 970263 550150 845230 101674 831878 587433 808747 > 388 [i]