Best Known (71, 102, s)-Nets in Base 2
(71, 102, 72)-Net over F2 — Constructive and digital
Digital (71, 102, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 34, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
(71, 102, 101)-Net over F2 — Digital
Digital (71, 102, 101)-net over F2, using
(71, 102, 661)-Net in Base 2 — Upper bound on s
There is no (71, 102, 662)-net in base 2, because
- 1 times m-reduction [i] would yield (71, 101, 662)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 548823 919523 334511 091476 051648 > 2101 [i]