Best Known (85, 237, s)-Nets in Base 2
(85, 237, 52)-Net over F2 — Constructive and digital
Digital (85, 237, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-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 3 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]
(85, 237, 57)-Net over F2 — Digital
Digital (85, 237, 57)-net over F2, using
- t-expansion [i] based on digital (83, 237, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(85, 237, 158)-Net in Base 2 — Upper bound on s
There is no (85, 237, 159)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 279553 222579 780356 824941 964319 589936 276619 283392 626453 908202 744933 093950 > 2237 [i]