Best Known (70, 70+125, s)-Nets in Base 2
(70, 70+125, 49)-Net over F2 — Constructive and digital
Digital (70, 195, 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]
(70, 70+125, 132)-Net in Base 2 — Upper bound on s
There is no (70, 195, 133)-net in base 2, because
- 1 times m-reduction [i] would yield (70, 194, 133)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 33546 010262 775339 003847 727784 027484 503215 682224 517178 328576 > 2194 [i]