Best Known (107, 107+33, s)-Nets in Base 2
(107, 107+33, 144)-Net over F2 — Constructive and digital
Digital (107, 140, 144)-net over F2, using
- 4 times m-reduction [i] based on digital (107, 144, 144)-net over F2, using
- trace code for nets [i] based on digital (11, 48, 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, 48, 48)-net over F8, using
(107, 107+33, 244)-Net over F2 — Digital
Digital (107, 140, 244)-net over F2, using
(107, 107+33, 2780)-Net in Base 2 — Upper bound on s
There is no (107, 140, 2781)-net in base 2, because
- 1 times m-reduction [i] would yield (107, 139, 2781)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 699595 705679 581753 121240 308871 020199 431255 > 2139 [i]