Best Known (123−78, 123, s)-Nets in Base 2
(123−78, 123, 34)-Net over F2 — Constructive and digital
Digital (45, 123, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(123−78, 123, 88)-Net in Base 2 — Upper bound on s
There is no (45, 123, 89)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 13 404485 952326 091527 843523 292904 980480 > 2123 [i]