Best Known (200−89, 200, s)-Nets in Base 2
(200−89, 200, 57)-Net over F2 — Constructive and digital
Digital (111, 200, 57)-net over F2, using
- t-expansion [i] based on digital (110, 200, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(200−89, 200, 72)-Net over F2 — Digital
Digital (111, 200, 72)-net over F2, using
- t-expansion [i] based on digital (110, 200, 72)-net over F2, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 110 and N(F) ≥ 72, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
(200−89, 200, 293)-Net in Base 2 — Upper bound on s
There is no (111, 200, 294)-net in base 2, because
- 1 times m-reduction [i] would yield (111, 199, 294)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2199, 294, S2, 88), but
- 5 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
- 5 times code embedding in larger space [i] would yield OA(2204, 299, S2, 88), but
- extracting embedded orthogonal array [i] would yield OA(2199, 294, S2, 88), but