Best Known (112, 223, s)-Nets in Base 2
(112, 223, 57)-Net over F2 — Constructive and digital
Digital (112, 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
(112, 223, 72)-Net over F2 — Digital
Digital (112, 223, 72)-net over F2, using
- t-expansion [i] based on digital (110, 223, 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
(112, 223, 236)-Net in Base 2 — Upper bound on s
There is no (112, 223, 237)-net in base 2, because
- 5 times m-reduction [i] would yield (112, 218, 237)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2218, 237, S2, 106), but
- the linear programming bound shows that M ≥ 59311 882667 731407 548267 433191 443187 482001 717729 589259 458427 942548 275200 / 110349 > 2218 [i]
- extracting embedded orthogonal array [i] would yield OA(2218, 237, S2, 106), but