Best Known (123, 166, s)-Nets in Base 2
(123, 166, 144)-Net over F2 — Constructive and digital
Digital (123, 166, 144)-net over F2, using
- 2 times m-reduction [i] based on digital (123, 168, 144)-net over F2, using
- trace code for nets [i] based on digital (11, 56, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- trace code for nets [i] based on digital (11, 56, 48)-net over F8, using
(123, 166, 220)-Net over F2 — Digital
Digital (123, 166, 220)-net over F2, using
(123, 166, 1981)-Net in Base 2 — Upper bound on s
There is no (123, 166, 1982)-net in base 2, because
- 1 times m-reduction [i] would yield (123, 165, 1982)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 46 924260 993484 279161 697730 380887 764460 848600 097829 > 2165 [i]