Best Known (197−88, 197, s)-Nets in Base 2
(197−88, 197, 56)-Net over F2 — Constructive and digital
Digital (109, 197, 56)-net over F2, using
- t-expansion [i] based on digital (105, 197, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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 (105, 55)-sequence over F2, using
(197−88, 197, 71)-Net over F2 — Digital
Digital (109, 197, 71)-net over F2, using
(197−88, 197, 291)-Net in Base 2 — Upper bound on s
There is no (109, 197, 292)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2197, 292, S2, 88), but
- 7 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
- 7 times code embedding in larger space [i] would yield OA(2204, 299, S2, 88), but