Best Known (213−178, 213, s)-Nets in Base 2
(213−178, 213, 24)-Net over F2 — Constructive and digital
Digital (35, 213, 24)-net over F2, using
- t-expansion [i] based on digital (33, 213, 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
(213−178, 213, 29)-Net over F2 — Digital
Digital (35, 213, 29)-net over F2, using
- net from sequence [i] based on digital (35, 28)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 35 and N(F) ≥ 29, using
(213−178, 213, 43)-Net in Base 2 — Upper bound on s
There is no (35, 213, 44)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(2213, 44, S2, 5, 178), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 738119 583382 486854 145868 719775 431240 291272 480414 276892 612085 415936 / 179 > 2213 [i]