Best Known (32, ∞, s)-Nets in Base 2
(32, ∞, 21)-Net over F2 — Constructive and digital
Digital (32, m, 21)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (32, 20)-sequence over F2, using
- t-expansion [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
- t-expansion [i] based on digital (21, 20)-sequence over F2, using
(32, ∞, 27)-Net over F2 — Digital
Digital (32, m, 27)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (32, 26)-sequence over F2, using
- t-expansion [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
- t-expansion [i] based on digital (31, 26)-sequence over F2, using
(32, ∞, 40)-Net in Base 2 — Upper bound on s
There is no (32, m, 41)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (32, 197, 41)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2197, 41, S2, 5, 165), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 479787 508978 388168 732564 061923 369929 005334 428502 117605 965824 / 83 > 2197 [i]
- extracting embedded OOA [i] would yield OOA(2197, 41, S2, 5, 165), but