Best Known (109, 109+93, s)-Nets in Base 2
(109, 109+93, 56)-Net over F2 — Constructive and digital
Digital (109, 202, 56)-net over F2, using
- t-expansion [i] based on digital (105, 202, 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
(109, 109+93, 67)-Net over F2 — Digital
Digital (109, 202, 67)-net over F2, using
(109, 109+93, 288)-Net in Base 2 — Upper bound on s
There is no (109, 202, 289)-net in base 2, because
- 1 times m-reduction [i] would yield (109, 201, 289)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2201, 289, S2, 92), but
- 11 times code embedding in larger space [i] would yield OA(2212, 300, S2, 92), but
- the linear programming bound shows that M ≥ 2484 132694 351399 471861 447697 940992 402712 231248 004226 234322 576635 442083 069406 167011 327832 607273 517056 / 377277 818302 855799 777736 052112 623275 > 2212 [i]
- 11 times code embedding in larger space [i] would yield OA(2212, 300, S2, 92), but
- extracting embedded orthogonal array [i] would yield OA(2201, 289, S2, 92), but