Best Known (114, 114+107, s)-Nets in Base 2
(114, 114+107, 57)-Net over F2 — Constructive and digital
Digital (114, 221, 57)-net over F2, using
- t-expansion [i] based on digital (110, 221, 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
(114, 114+107, 73)-Net over F2 — Digital
Digital (114, 221, 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
(114, 114+107, 242)-Net in Base 2 — Upper bound on s
There is no (114, 221, 243)-net in base 2, because
- 3 times m-reduction [i] would yield (114, 218, 243)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2218, 243, S2, 104), but
- the linear programming bound shows that M ≥ 84 817286 292295 936024 732573 480487 935041 534790 936244 922973 031050 817325 498368 / 163 213765 > 2218 [i]
- extracting embedded orthogonal array [i] would yield OA(2218, 243, S2, 104), but