Best Known (134−38, 134, s)-Nets in Base 9
(134−38, 134, 776)-Net over F9 — Constructive and digital
Digital (96, 134, 776)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 26, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- digital (70, 108, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 54, 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, 54, 370)-net over F81, using
- digital (7, 26, 36)-net over F9, using
(134−38, 134, 5963)-Net over F9 — Digital
Digital (96, 134, 5963)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9134, 5963, F9, 38) (dual of [5963, 5829, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(9134, 6566, F9, 38) (dual of [6566, 6432, 39]-code), using
- 1 times code embedding in larger space [i] based on linear OA(9133, 6565, F9, 38) (dual of [6565, 6432, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- linear OA(9133, 6561, F9, 38) (dual of [6561, 6428, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(9129, 6561, F9, 37) (dual of [6561, 6432, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(90, 4, F9, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(9133, 6565, F9, 38) (dual of [6565, 6432, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(9134, 6566, F9, 38) (dual of [6566, 6432, 39]-code), using
(134−38, 134, 5321639)-Net in Base 9 — Upper bound on s
There is no (96, 134, 5321640)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 73 874935 687466 185158 694588 231437 194966 515484 868725 278000 901651 354436 321423 839718 565716 921285 443813 910419 144279 176119 003075 451585 > 9134 [i]