Best Known (78−19, 78, s)-Nets in Base 2
(78−19, 78, 102)-Net over F2 — Constructive and digital
Digital (59, 78, 102)-net over F2, using
- trace code for nets [i] based on digital (7, 26, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
(78−19, 78, 147)-Net over F2 — Digital
Digital (59, 78, 147)-net over F2, using
(78−19, 78, 1547)-Net in Base 2 — Upper bound on s
There is no (59, 78, 1548)-net in base 2, because
- 1 times m-reduction [i] would yield (59, 77, 1548)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 151615 207354 961789 417009 > 277 [i]