Best Known (103, 103+86, s)-Nets in Base 2
(103, 103+86, 55)-Net over F2 — Constructive and digital
Digital (103, 189, 55)-net over F2, using
- t-expansion [i] based on digital (100, 189, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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 (100, 54)-sequence over F2, using
(103, 103+86, 66)-Net over F2 — Digital
Digital (103, 189, 66)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2189, 66, F2, 8, 86) (dual of [(66, 8), 339, 87]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2181, 65, F2, 8, 86) (dual of [(65, 8), 339, 87]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(8;F,433P) [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2181, 65, F2, 8, 86) (dual of [(65, 8), 339, 87]-NRT-code), using
(103, 103+86, 287)-Net in Base 2 — Upper bound on s
There is no (103, 189, 288)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2189, 288, S2, 86), but
- 11 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
- 11 times code embedding in larger space [i] would yield OA(2200, 299, S2, 86), but