Best Known (202−89, 202, s)-Nets in Base 2
(202−89, 202, 59)-Net over F2 — Constructive and digital
Digital (113, 202, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 59, 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, 143, 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, 59, 17)-net over F2, using
(202−89, 202, 75)-Net over F2 — Digital
Digital (113, 202, 75)-net over F2, using
(202−89, 202, 295)-Net in Base 2 — Upper bound on s
There is no (113, 202, 296)-net in base 2, because
- 1 times m-reduction [i] would yield (113, 201, 296)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2201, 296, S2, 88), but
- 3 times code embedding in larger space [i] would yield OA(2204, 299, S2, 88), but
- adding a parity check bit [i] would yield OA(2205, 300, S2, 89), but
- the linear programming bound shows that M ≥ 416927 463188 475542 795463 940731 898983 181308 104641 213119 598295 609827 594303 154474 074874 094714 331435 368448 / 5584 401256 756961 297780 513782 298869 514125 > 2205 [i]
- adding a parity check bit [i] would yield OA(2205, 300, S2, 89), but
- 3 times code embedding in larger space [i] would yield OA(2204, 299, S2, 88), but
- extracting embedded orthogonal array [i] would yield OA(2201, 296, S2, 88), but