Best Known (22, 22+72, s)-Nets in Base 2
(22, 22+72, 21)-Net over F2 — Constructive and digital
Digital (22, 94, 21)-net over F2, using
- t-expansion [i] based on digital (21, 94, 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
(22, 22+72, 32)-Net in Base 2 — Upper bound on s
There is no (22, 94, 33)-net in base 2, because
- 3 times m-reduction [i] would yield (22, 91, 33)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(291, 33, S2, 3, 69), but
- the LP bound with quadratic polynomials shows that M ≥ 316912 650057 057350 374175 801344 / 105 > 291 [i]
- extracting embedded OOA [i] would yield OOA(291, 33, S2, 3, 69), but