Best Known (138−43, 138, s)-Nets in Base 2
(138−43, 138, 72)-Net over F2 — Constructive and digital
Digital (95, 138, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 46, 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
(138−43, 138, 121)-Net over F2 — Digital
Digital (95, 138, 121)-net over F2, using
(138−43, 138, 768)-Net in Base 2 — Upper bound on s
There is no (95, 138, 769)-net in base 2, because
- 1 times m-reduction [i] would yield (95, 137, 769)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 178004 251761 544430 250334 839967 088869 480320 > 2137 [i]