Best Known (32, 32+21, s)-Nets in Base 81
(32, 32+21, 772)-Net over F81 — Constructive and digital
Digital (32, 53, 772)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- digital (20, 41, 656)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 656, F81, 21, 21) (dual of [(656, 21), 13735, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 10-folding and stacking with additional row [i] based on linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using
- net defined by OOA [i] based on linear OOA(8141, 656, F81, 21, 21) (dual of [(656, 21), 13735, 22]-NRT-code), using
- digital (2, 12, 116)-net over F81, using
(32, 32+21, 11860)-Net over F81 — Digital
Digital (32, 53, 11860)-net over F81, using
(32, 32+21, large)-Net in Base 81 — Upper bound on s
There is no (32, 53, large)-net in base 81, because
- 19 times m-reduction [i] would yield (32, 34, large)-net in base 81, but