Best Known (15, 15+55, s)-Nets in Base 7
(15, 15+55, 23)-Net over F7 — Constructive and digital
Digital (15, 70, 23)-net over F7, using
- net from sequence [i] based on digital (15, 22)-sequence over F7, using
(15, 15+55, 48)-Net over F7 — Digital
Digital (15, 70, 48)-net over F7, using
- t-expansion [i] based on digital (13, 70, 48)-net over F7, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
(15, 15+55, 240)-Net in Base 7 — Upper bound on s
There is no (15, 70, 241)-net in base 7, because
- 5 times m-reduction [i] would yield (15, 65, 241)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(765, 241, S7, 50), but
- the linear programming bound shows that M ≥ 22112 624364 978795 474538 754976 749930 094707 292079 021651 687603 190206 394263 161826 780561 387920 429787 399829 683425 235249 342283 395238 283264 / 2560 243716 514173 842701 937347 863769 540331 960625 883665 166806 472978 012051 423879 > 765 [i]
- extracting embedded orthogonal array [i] would yield OA(765, 241, S7, 50), but