Best Known (59, 59+82, s)-Nets in Base 2
(59, 59+82, 43)-Net over F2 — Constructive and digital
Digital (59, 141, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(59, 59+82, 122)-Net in Base 2 — Upper bound on s
There is no (59, 141, 123)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3 340668 086959 218981 372388 076824 177332 045084 > 2141 [i]