Best Known (204−89, 204, s)-Nets in Base 2
(204−89, 204, 60)-Net over F2 — Constructive and digital
Digital (115, 204, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 102, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
(204−89, 204, 77)-Net over F2 — Digital
Digital (115, 204, 77)-net over F2, using
(204−89, 204, 297)-Net in Base 2 — Upper bound on s
There is no (115, 204, 298)-net in base 2, because
- 1 times m-reduction [i] would yield (115, 203, 298)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2203, 298, S2, 88), but
- 1 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
- 1 times code embedding in larger space [i] would yield OA(2204, 299, S2, 88), but
- extracting embedded orthogonal array [i] would yield OA(2203, 298, S2, 88), but