Best Known (66−19, 66, s)-Nets in Base 81
(66−19, 66, 59165)-Net over F81 — Constructive and digital
Digital (47, 66, 59165)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 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 (36, 55, 59049)-net over F81, using
- net defined by OOA [i] based on linear OOA(8155, 59049, F81, 19, 19) (dual of [(59049, 19), 1121876, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using
- net defined by OOA [i] based on linear OOA(8155, 59049, F81, 19, 19) (dual of [(59049, 19), 1121876, 20]-NRT-code), using
- digital (2, 11, 116)-net over F81, using
(66−19, 66, 939340)-Net over F81 — Digital
Digital (47, 66, 939340)-net over F81, using
(66−19, 66, large)-Net in Base 81 — Upper bound on s
There is no (47, 66, large)-net in base 81, because
- 17 times m-reduction [i] would yield (47, 49, large)-net in base 81, but