Best Known (207−99, 207, s)-Nets in Base 2
(207−99, 207, 56)-Net over F2 — Constructive and digital
Digital (108, 207, 56)-net over F2, using
- t-expansion [i] based on 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]
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
(207−99, 207, 65)-Net over F2 — Digital
Digital (108, 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
(207−99, 207, 282)-Net in Base 2 — Upper bound on s
There is no (108, 207, 283)-net in base 2, because
- 1 times m-reduction [i] would yield (108, 206, 283)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2206, 283, S2, 98), but
- 17 times code embedding in larger space [i] would yield OA(2223, 300, S2, 98), but
- the linear programming bound shows that M ≥ 1 797227 776840 883681 896516 291018 079602 556004 736527 384481 376471 307374 972535 986485 205069 933364 379648 / 112622 624143 760877 566730 935625 > 2223 [i]
- 17 times code embedding in larger space [i] would yield OA(2223, 300, S2, 98), but
- extracting embedded orthogonal array [i] would yield OA(2206, 283, S2, 98), but