Best Known (37, 37+191, s)-Nets in Base 2
(37, 37+191, 24)-Net over F2 — Constructive and digital
Digital (37, 228, 24)-net over F2, using
- t-expansion [i] based on digital (33, 228, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(37, 37+191, 30)-Net over F2 — Digital
Digital (37, 228, 30)-net over F2, using
- t-expansion [i] based on digital (36, 228, 30)-net over F2, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 36 and N(F) ≥ 30, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
(37, 37+191, 45)-Net in Base 2 — Upper bound on s
There is no (37, 228, 46)-net in base 2, because
- 5 times m-reduction [i] would yield (37, 223, 46)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2223, 46, S2, 5, 186), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2695 994666 715063 979466 701508 701963 067363 714442 254057 248110 361024 921600 / 187 > 2223 [i]
- extracting embedded OOA [i] would yield OOA(2223, 46, S2, 5, 186), but