Best Known (205−102, 205, s)-Nets in Base 2
(205−102, 205, 55)-Net over F2 — Constructive and digital
Digital (103, 205, 55)-net over F2, using
- t-expansion [i] based on digital (100, 205, 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
(205−102, 205, 65)-Net over F2 — Digital
Digital (103, 205, 65)-net over F2, using
- t-expansion [i] based on digital (95, 205, 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
(205−102, 205, 217)-Net in Base 2 — Upper bound on s
There is no (103, 205, 218)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2205, 218, S2, 102), but
- the linear programming bound shows that M ≥ 272331 004236 659599 976647 399713 241508 574642 785762 357467 384194 793472 / 3835 > 2205 [i]