Best Known (111, 111+141, s)-Nets in Base 2
(111, 111+141, 57)-Net over F2 — Constructive and digital
Digital (111, 252, 57)-net over F2, using
- t-expansion [i] based on digital (110, 252, 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
(111, 111+141, 72)-Net over F2 — Digital
Digital (111, 252, 72)-net over F2, using
- t-expansion [i] based on digital (110, 252, 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
(111, 111+141, 231)-Net in Base 2 — Upper bound on s
There is no (111, 252, 232)-net in base 2, because
- 1 times m-reduction [i] would yield (111, 251, 232)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3936 679115 734962 996262 348066 434429 239017 314084 980329 629156 132590 861779 110903 > 2251 [i]