Best Known (207−102, 207, s)-Nets in Base 2
(207−102, 207, 56)-Net over F2 — Constructive and digital
Digital (105, 207, 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]
(207−102, 207, 65)-Net over F2 — Digital
Digital (105, 207, 65)-net over F2, using
- t-expansion [i] based on digital (95, 207, 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
(207−102, 207, 222)-Net in Base 2 — Upper bound on s
There is no (105, 207, 223)-net in base 2, because
- 2 times m-reduction [i] would yield (105, 205, 223)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2205, 223, S2, 100), but
- the linear programming bound shows that M ≥ 3311 860948 392786 407276 126134 596067 755564 612960 156468 450725 571621 552128 / 60 276645 > 2205 [i]
- extracting embedded orthogonal array [i] would yield OA(2205, 223, S2, 100), but