Best Known (258−233, 258, s)-Nets in Base 2
(258−233, 258, 21)-Net over F2 — Constructive and digital
Digital (25, 258, 21)-net over F2, using
- t-expansion [i] based on digital (21, 258, 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
(258−233, 258, 24)-Net over F2 — Digital
Digital (25, 258, 24)-net over F2, using
- net from sequence [i] based on digital (25, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 25 and N(F) ≥ 24, using
(258−233, 258, 32)-Net in Base 2 — Upper bound on s
There is no (25, 258, 33)-net in base 2, because
- 67 times m-reduction [i] would yield (25, 191, 33)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2191, 33, S2, 6, 166), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 596324 664861 734672 564399 995204 728309 529723 767224 083278 725120 / 167 > 2191 [i]
- extracting embedded OOA [i] would yield OOA(2191, 33, S2, 6, 166), but