Best Known (209−101, 209, s)-Nets in Base 2
(209−101, 209, 56)-Net over F2 — Constructive and digital
Digital (108, 209, 56)-net over F2, using
- t-expansion [i] based on digital (105, 209, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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 (105, 55)-sequence over F2, using
(209−101, 209, 65)-Net over F2 — Digital
Digital (108, 209, 65)-net over F2, using
- t-expansion [i] based on digital (95, 209, 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
(209−101, 209, 230)-Net in Base 2 — Upper bound on s
There is no (108, 209, 231)-net in base 2, because
- 1 times m-reduction [i] would yield (108, 208, 231)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2208, 231, S2, 100), but
- the linear programming bound shows that M ≥ 233249 033580 853850 928523 181090 679150 953723 061936 188989 177608 090998 013952 / 564 257421 > 2208 [i]
- extracting embedded orthogonal array [i] would yield OA(2208, 231, S2, 100), but