Best Known (39, 39+24, s)-Nets in Base 81
(39, 39+24, 740)-Net over F81 — Constructive and digital
Digital (39, 63, 740)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (11, 23, 1093)-net over F81, using
- net defined by OOA [i] based on linear OOA(8123, 1093, F81, 12, 12) (dual of [(1093, 12), 13093, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(8123, 6558, F81, 12) (dual of [6558, 6535, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(8123, 6558, F81, 12) (dual of [6558, 6535, 13]-code), using
- net defined by OOA [i] based on linear OOA(8123, 1093, F81, 12, 12) (dual of [(1093, 12), 13093, 13]-NRT-code), using
- digital (16, 40, 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
- digital (11, 23, 1093)-net over F81, using
(39, 39+24, 19916)-Net over F81 — Digital
Digital (39, 63, 19916)-net over F81, using
(39, 39+24, large)-Net in Base 81 — Upper bound on s
There is no (39, 63, large)-net in base 81, because
- 22 times m-reduction [i] would yield (39, 41, large)-net in base 81, but