Best Known (96, 116, s)-Nets in Base 3
(96, 116, 688)-Net over F3 — Constructive and digital
Digital (96, 116, 688)-net over F3, using
- t-expansion [i] based on digital (94, 116, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 29, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 29, 172)-net over F81, using
(96, 116, 4204)-Net over F3 — Digital
Digital (96, 116, 4204)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3116, 4204, F3, 20) (dual of [4204, 4088, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3116, 6602, F3, 20) (dual of [6602, 6486, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(3105, 6561, F3, 20) (dual of [6561, 6456, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(311, 41, F3, 5) (dual of [41, 30, 6]-code), using
- (u, u+v)-construction [i] based on
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- (u, u+v)-construction [i] based on
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3116, 6602, F3, 20) (dual of [6602, 6486, 21]-code), using
(96, 116, 775438)-Net in Base 3 — Upper bound on s
There is no (96, 116, 775439)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 22 185362 320282 891833 898390 503608 163577 130801 768542 142477 > 3116 [i]