Best Known (72, 72+96, s)-Nets in Base 2
(72, 72+96, 49)-Net over F2 — Constructive and digital
Digital (72, 168, 49)-net over F2, using
- t-expansion [i] based on digital (70, 168, 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
(72, 72+96, 149)-Net in Base 2 — Upper bound on s
There is no (72, 168, 150)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 384 581271 121494 514746 581166 554660 230418 843144 567892 > 2168 [i]