Best Known (224−107, 224, s)-Nets in Base 2
(224−107, 224, 57)-Net over F2 — Constructive and digital
Digital (117, 224, 57)-net over F2, using
- t-expansion [i] based on digital (110, 224, 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
(224−107, 224, 73)-Net over F2 — Digital
Digital (117, 224, 73)-net over F2, using
- t-expansion [i] based on digital (114, 224, 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
(224−107, 224, 248)-Net in Base 2 — Upper bound on s
There is no (117, 224, 249)-net in base 2, because
- 1 times m-reduction [i] would yield (117, 223, 249)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2223, 249, S2, 106), but
- the linear programming bound shows that M ≥ 125060 361585 465082 046951 669439 069378 009061 149491 060510 099746 675837 762518 646784 / 7177 430007 > 2223 [i]
- extracting embedded orthogonal array [i] would yield OA(2223, 249, S2, 106), but