Best Known (15, 15+90, s)-Nets in Base 8
(15, 15+90, 65)-Net over F8 — Constructive and digital
Digital (15, 105, 65)-net over F8, using
- t-expansion [i] based on digital (14, 105, 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
(15, 15+90, 127)-Net in Base 8 — Upper bound on s
There is no (15, 105, 128)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(8105, 128, S8, 90), but
- the linear programming bound shows that M ≥ 21950 796382 814438 782744 864463 381336 127596 030073 856912 690696 782531 039738 810829 256630 497562 292754 935128 215485 677031 129088 / 296811 395949 608374 280875 > 8105 [i]