Best Known (213−102, 213, s)-Nets in Base 2
(213−102, 213, 57)-Net over F2 — Constructive and digital
Digital (111, 213, 57)-net over F2, using
- t-expansion [i] based on digital (110, 213, 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
(213−102, 213, 72)-Net over F2 — Digital
Digital (111, 213, 72)-net over F2, using
- t-expansion [i] based on digital (110, 213, 72)-net over F2, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 110 and N(F) ≥ 72, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
(213−102, 213, 236)-Net in Base 2 — Upper bound on s
There is no (111, 213, 237)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2213, 237, S2, 102), but
- the linear programming bound shows that M ≥ 56 509947 626840 275107 041347 271940 448571 860758 301585 684224 163749 835147 575296 / 3905 092295 > 2213 [i]