Best Known (59−24, 59, s)-Nets in Base 81
(59−24, 59, 628)-Net over F81 — Constructive and digital
Digital (35, 59, 628)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 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
- digital (23, 47, 546)-net over F81, using
- net defined by OOA [i] based on linear OOA(8147, 546, F81, 24, 24) (dual of [(546, 24), 13057, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8147, 6552, F81, 24) (dual of [6552, 6505, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8147, 6552, F81, 24) (dual of [6552, 6505, 25]-code), using
- net defined by OOA [i] based on linear OOA(8147, 546, F81, 24, 24) (dual of [(546, 24), 13057, 25]-NRT-code), using
- digital (0, 12, 82)-net over F81, using
(59−24, 59, 9281)-Net over F81 — Digital
Digital (35, 59, 9281)-net over F81, using
(59−24, 59, large)-Net in Base 81 — Upper bound on s
There is no (35, 59, large)-net in base 81, because
- 22 times m-reduction [i] would yield (35, 37, large)-net in base 81, but