Best Known (17, 17+27, s)-Nets in Base 2
(17, 17+27, 17)-Net over F2 — Constructive and digital
Digital (17, 44, 17)-net over F2, using
- t-expansion [i] based on digital (15, 44, 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
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
(17, 17+27, 39)-Net in Base 2 — Upper bound on s
There is no (17, 44, 40)-net in base 2, because
- 1 times m-reduction [i] would yield (17, 43, 40)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 9 673849 095708 > 243 [i]