Best Known (83−37, 83, s)-Nets in Base 2
(83−37, 83, 34)-Net over F2 — Constructive and digital
Digital (46, 83, 34)-net over F2, using
- t-expansion [i] based on digital (45, 83, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
(83−37, 83, 36)-Net over F2 — Digital
Digital (46, 83, 36)-net over F2, using
(83−37, 83, 143)-Net in Base 2 — Upper bound on s
There is no (46, 83, 144)-net in base 2, because
- 1 times m-reduction [i] would yield (46, 82, 144)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(282, 144, S2, 36), but
- the linear programming bound shows that M ≥ 2893 609949 429043 518839 097243 777165 200630 895720 113073 291264 / 558 874024 262522 794899 259597 123083 > 282 [i]
- extracting embedded orthogonal array [i] would yield OA(282, 144, S2, 36), but