Best Known (92, 96, s)-Nets in Base 3
(92, 96, large)-Net over F3 — Constructive and digital
Digital (92, 96, large)-net over F3, using
- t-expansion [i] based on digital (89, 96, large)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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 (86, 93, 8388600)-net over F3, using
- trace code for nets [i] based on digital (24, 31, 2796200)-net over F27, using
- net defined by OOA [i] based on linear OOA(2731, 2796200, F27, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2731, 8388601, F27, 7) (dual of [8388601, 8388570, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2731, 8388601, F27, 7) (dual of [8388601, 8388570, 8]-code), using
- net defined by OOA [i] based on linear OOA(2731, 2796200, F27, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- trace code for nets [i] based on digital (24, 31, 2796200)-net over F27, using
- digital (0, 3, 4)-net over F3, using
- (u, u+v)-construction [i] based on
(92, 96, large)-Net in Base 3 — Upper bound on s
There is no (92, 96, large)-net in base 3, because
- 2 times m-reduction [i] would yield (92, 94, large)-net in base 3, but