Best Known (82−70, 82, s)-Nets in Base 9
(82−70, 82, 40)-Net over F9 — Constructive and digital
Digital (12, 82, 40)-net over F9, using
- t-expansion [i] based on digital (8, 82, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(82−70, 82, 56)-Net over F9 — Digital
Digital (12, 82, 56)-net over F9, using
- net from sequence [i] based on digital (12, 55)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 12 and N(F) ≥ 56, using
(82−70, 82, 257)-Net in Base 9 — Upper bound on s
There is no (12, 82, 258)-net in base 9, because
- 17 times m-reduction [i] would yield (12, 65, 258)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(965, 258, S9, 53), but
- the linear programming bound shows that M ≥ 3115 168854 220783 215219 768780 159936 720843 927087 163333 700130 000830 275274 104131 449440 559940 656772 807198 649003 636302 225680 570591 397494 949207 472122 873600 / 27 533585 604222 238879 620126 549314 600127 207589 391129 267721 230267 333962 835368 350738 616937 > 965 [i]
- extracting embedded orthogonal array [i] would yield OA(965, 258, S9, 53), but