Best Known (189−116, 189, s)-Nets in Base 2
(189−116, 189, 49)-Net over F2 — Constructive and digital
Digital (73, 189, 49)-net over F2, using
- t-expansion [i] based on digital (70, 189, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [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 (70, 48)-sequence over F2, using
(189−116, 189, 141)-Net in Base 2 — Upper bound on s
There is no (73, 189, 142)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 899 033219 910238 852478 282008 051376 996791 542594 627427 800080 > 2189 [i]