Best Known (253−141, 253, s)-Nets in Base 2
(253−141, 253, 57)-Net over F2 — Constructive and digital
Digital (112, 253, 57)-net over F2, using
- t-expansion [i] based on digital (110, 253, 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
(253−141, 253, 72)-Net over F2 — Digital
Digital (112, 253, 72)-net over F2, using
- t-expansion [i] based on digital (110, 253, 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
(253−141, 253, 234)-Net in Base 2 — Upper bound on s
There is no (112, 253, 235)-net in base 2, because
- 1 times m-reduction [i] would yield (112, 252, 235)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7691 245391 386056 349166 901571 610679 242434 100382 694756 830719 846385 376048 032818 > 2252 [i]