Best Known (117−100, 117, s)-Nets in Base 8
(117−100, 117, 65)-Net over F8 — Constructive and digital
Digital (17, 117, 65)-net over F8, using
- t-expansion [i] based on digital (14, 117, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(117−100, 117, 139)-Net in Base 8 — Upper bound on s
There is no (17, 117, 140)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(8117, 140, S8, 100), but
- the linear programming bound shows that M ≥ 2 610180 317140 959157 407235 870225 536882 213600 222274 356475 248057 654929 251624 957834 778793 578988 176724 604529 956295 515201 688207 097856 / 534 269890 876318 386075 > 8117 [i]