Best Known (72, 72+111, s)-Nets in Base 2
(72, 72+111, 49)-Net over F2 — Constructive and digital
Digital (72, 183, 49)-net over F2, using
- t-expansion [i] based on digital (70, 183, 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+111, 141)-Net in Base 2 — Upper bound on s
There is no (72, 183, 142)-net in base 2, because
- 1 times m-reduction [i] would yield (72, 182, 142)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 6 887250 228858 821734 921059 575449 708553 756074 472137 712960 > 2182 [i]