Best Known (218−102, 218, s)-Nets in Base 2
(218−102, 218, 57)-Net over F2 — Constructive and digital
Digital (116, 218, 57)-net over F2, using
- t-expansion [i] based on digital (110, 218, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(218−102, 218, 73)-Net over F2 — Digital
Digital (116, 218, 73)-net over F2, using
- t-expansion [i] based on digital (114, 218, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
(218−102, 218, 249)-Net in Base 2 — Upper bound on s
There is no (116, 218, 250)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2218, 250, S2, 102), but
- the linear programming bound shows that M ≥ 1373 805119 743915 279785 752879 881242 293419 025808 545527 502630 731678 822405 505024 / 2797 932267 > 2218 [i]