Best Known (42−27, 42, s)-Nets in Base 2
(42−27, 42, 17)-Net over F2 — Constructive and digital
Digital (15, 42, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
(42−27, 42, 34)-Net in Base 2 — Upper bound on s
There is no (15, 42, 35)-net in base 2, because
- 1 times m-reduction [i] would yield (15, 41, 35)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 748971 589888 > 241 [i]