Best Known (63, 63+56, s)-Nets in Base 2
(63, 63+56, 43)-Net over F2 — Constructive and digital
Digital (63, 119, 43)-net over F2, using
- t-expansion [i] based on digital (59, 119, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(63, 63+56, 44)-Net over F2 — Digital
Digital (63, 119, 44)-net over F2, using
- t-expansion [i] based on digital (62, 119, 44)-net over F2, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 62 and N(F) ≥ 44, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
(63, 63+56, 145)-Net in Base 2 — Upper bound on s
There is no (63, 119, 146)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2119, 146, S2, 56), but
- the linear programming bound shows that M ≥ 5165 551323 791927 774620 548045 364260 917630 468096 / 7704 797749 > 2119 [i]