Best Known (202−179, 202, s)-Nets in Base 2
(202−179, 202, 21)-Net over F2 — Constructive and digital
Digital (23, 202, 21)-net over F2, using
- t-expansion [i] based on digital (21, 202, 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
(202−179, 202, 22)-Net over F2 — Digital
Digital (23, 202, 22)-net over F2, using
- net from sequence [i] based on digital (23, 21)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 23 and N(F) ≥ 22, using
(202−179, 202, 30)-Net in Base 2 — Upper bound on s
There is no (23, 202, 31)-net in base 2, because
- 54 times m-reduction [i] would yield (23, 148, 31)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2148, 31, S2, 5, 125), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7849 862309 882779 345820 572831 972223 250105 106432 / 21 > 2148 [i]
- extracting embedded OOA [i] would yield OOA(2148, 31, S2, 5, 125), but