Best Known (117, 214, s)-Nets in Base 2
(117, 214, 59)-Net over F2 — Constructive and digital
Digital (117, 214, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 63, 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, 151, 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, 63, 17)-net over F2, using
(117, 214, 73)-Net over F2 — Digital
Digital (117, 214, 73)-net over F2, using
- t-expansion [i] based on digital (114, 214, 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
(117, 214, 292)-Net in Base 2 — Upper bound on s
There is no (117, 214, 293)-net in base 2, because
- 1 times m-reduction [i] would yield (117, 213, 293)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2213, 293, S2, 96), but
- 6 times code embedding in larger space [i] would yield OA(2219, 299, S2, 96), but
- adding a parity check bit [i] would yield OA(2220, 300, S2, 97), but
- the linear programming bound shows that M ≥ 2 707506 179671 220537 436761 186277 555172 982275 381427 765331 317661 637213 928123 767152 572244 071765 637582 553088 / 1 434637 915544 533146 412054 075529 090625 > 2220 [i]
- adding a parity check bit [i] would yield OA(2220, 300, S2, 97), but
- 6 times code embedding in larger space [i] would yield OA(2219, 299, S2, 96), but
- extracting embedded orthogonal array [i] would yield OA(2213, 293, S2, 96), but