Best Known (92, 149, s)-Nets in Base 2
(92, 149, 66)-Net over F2 — Constructive and digital
Digital (92, 149, 66)-net over F2, using
- 5 times m-reduction [i] based on digital (92, 154, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 77, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 77, 33)-net over F4, using
(92, 149, 80)-Net over F2 — Digital
Digital (92, 149, 80)-net over F2, using
- 1 times m-reduction [i] based on digital (92, 150, 80)-net over F2, using
- trace code for nets [i] based on digital (17, 75, 40)-net over F4, using
- net from sequence [i] based on digital (17, 39)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 17 and N(F) ≥ 40, using
- net from sequence [i] based on digital (17, 39)-sequence over F4, using
- trace code for nets [i] based on digital (17, 75, 40)-net over F4, using
(92, 149, 400)-Net in Base 2 — Upper bound on s
There is no (92, 149, 401)-net in base 2, because
- 1 times m-reduction [i] would yield (92, 148, 401)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 358 691003 871568 671975 820266 457967 362265 210784 > 2148 [i]