Best Known (50−48, 50, s)-Nets in Base 7
(50−48, 50, 10)-Net over F7 — Constructive and digital
Digital (2, 50, 10)-net over F7, using
- net from sequence [i] based on digital (2, 9)-sequence over F7, using
(50−48, 50, 16)-Net over F7 — Digital
Digital (2, 50, 16)-net over F7, using
- net from sequence [i] based on digital (2, 15)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 2 and N(F) ≥ 16, using
(50−48, 50, 20)-Net in Base 7 — Upper bound on s
There is no (2, 50, 21)-net in base 7, because
- 26 times m-reduction [i] would yield (2, 24, 21)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(724, 21, S7, 2, 22), but
- the linear programming bound for OOAs shows that M ≥ 185642 213207 768855 554569 / 961 > 724 [i]
- extracting embedded OOA [i] would yield OOA(724, 21, S7, 2, 22), but