Best Known (253−209, 253, s)-Nets in Base 2
(253−209, 253, 33)-Net over F2 — Constructive and digital
Digital (44, 253, 33)-net over F2, using
- t-expansion [i] based on digital (39, 253, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(253−209, 253, 34)-Net over F2 — Digital
Digital (44, 253, 34)-net over F2, using
- t-expansion [i] based on digital (43, 253, 34)-net over F2, using
- net from sequence [i] based on digital (43, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 43 and N(F) ≥ 34, using
- net from sequence [i] based on digital (43, 33)-sequence over F2, using
(253−209, 253, 54)-Net in Base 2 — Upper bound on s
There is no (44, 253, 55)-net in base 2, because
- 40 times m-reduction [i] would yield (44, 213, 55)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2213, 55, S2, 4, 169), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 263280 729171 392966 744795 069209 176080 797237 738501 372778 135777 443840 / 17 > 2213 [i]
- extracting embedded OOA [i] would yield OOA(2213, 55, S2, 4, 169), but