Best Known (210−109, 210, s)-Nets in Base 2
(210−109, 210, 55)-Net over F2 — Constructive and digital
Digital (101, 210, 55)-net over F2, using
- t-expansion [i] based on digital (100, 210, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 6 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (100, 54)-sequence over F2, using
(210−109, 210, 65)-Net over F2 — Digital
Digital (101, 210, 65)-net over F2, using
- t-expansion [i] based on digital (95, 210, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(210−109, 210, 213)-Net in Base 2 — Upper bound on s
There is no (101, 210, 214)-net in base 2, because
- 9 times m-reduction [i] would yield (101, 201, 214)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2201, 214, S2, 100), but
- the linear programming bound shows that M ≥ 128760 731610 384372 798626 338535 112677 014899 081485 827624 307028 656128 / 29087 > 2201 [i]
- extracting embedded orthogonal array [i] would yield OA(2201, 214, S2, 100), but