Best Known (31, 31+77, s)-Nets in Base 2
(31, 31+77, 21)-Net over F2 — Constructive and digital
Digital (31, 108, 21)-net over F2, using
- t-expansion [i] based on digital (21, 108, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(31, 31+77, 27)-Net over F2 — Digital
Digital (31, 108, 27)-net over F2, using
- net from sequence [i] based on digital (31, 26)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 31 and N(F) ≥ 27, using
(31, 31+77, 49)-Net in Base 2 — Upper bound on s
There is no (31, 108, 50)-net in base 2, because
- 15 times m-reduction [i] would yield (31, 93, 50)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(293, 50, S2, 2, 62), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 633825 300114 114700 748351 602688 / 63 > 293 [i]
- extracting embedded OOA [i] would yield OOA(293, 50, S2, 2, 62), but