Best Known (195−87, 195, s)-Nets in Base 2
(195−87, 195, 56)-Net over F2 — Constructive and digital
Digital (108, 195, 56)-net over F2, using
- t-expansion [i] based on digital (105, 195, 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
(195−87, 195, 70)-Net over F2 — Digital
Digital (108, 195, 70)-net over F2, using
(195−87, 195, 292)-Net in Base 2 — Upper bound on s
There is no (108, 195, 293)-net in base 2, because
- 1 times m-reduction [i] would yield (108, 194, 293)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2194, 293, S2, 86), but
- 6 times code embedding in larger space [i] would yield OA(2200, 299, S2, 86), but
- adding a parity check bit [i] would yield OA(2201, 300, S2, 87), but
- the linear programming bound shows that M ≥ 6062 729839 358588 077129 287653 744482 312929 554681 473387 231550 995785 979703 893542 676711 534073 403563 590830 522368 / 1273 266655 863433 158102 727954 895995 795355 723661 > 2201 [i]
- adding a parity check bit [i] would yield OA(2201, 300, S2, 87), but
- 6 times code embedding in larger space [i] would yield OA(2200, 299, S2, 86), but
- extracting embedded orthogonal array [i] would yield OA(2194, 293, S2, 86), but