Best Known (217−99, 217, s)-Nets in Base 2
(217−99, 217, 59)-Net over F2 — Constructive and digital
Digital (118, 217, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 64, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- digital (54, 153, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (15, 64, 17)-net over F2, using
(217−99, 217, 73)-Net over F2 — Digital
Digital (118, 217, 73)-net over F2, using
- t-expansion [i] based on digital (114, 217, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
(217−99, 217, 292)-Net in Base 2 — Upper bound on s
There is no (118, 217, 293)-net in base 2, because
- 1 times m-reduction [i] would yield (118, 216, 293)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2216, 293, S2, 98), but
- 7 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]
- 7 times code embedding in larger space [i] would yield OA(2223, 300, S2, 98), but
- extracting embedded orthogonal array [i] would yield OA(2216, 293, S2, 98), but