Best Known (223−104, 223, s)-Nets in Base 2
(223−104, 223, 57)-Net over F2 — Constructive and digital
Digital (119, 223, 57)-net over F2, using
- t-expansion [i] based on digital (110, 223, 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
(223−104, 223, 73)-Net over F2 — Digital
Digital (119, 223, 73)-net over F2, using
- t-expansion [i] based on digital (114, 223, 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
(223−104, 223, 258)-Net in Base 2 — Upper bound on s
There is no (119, 223, 259)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2223, 259, S2, 104), but
- the linear programming bound shows that M ≥ 7 781600 075113 312775 337502 159004 327439 936028 728612 302400 844627 501716 281730 531328 / 421052 504375 > 2223 [i]