Best Known (120−92, 120, s)-Nets in Base 2
(120−92, 120, 21)-Net over F2 — Constructive and digital
Digital (28, 120, 21)-net over F2, using
- t-expansion [i] based on digital (21, 120, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(120−92, 120, 25)-Net over F2 — Digital
Digital (28, 120, 25)-net over F2, using
- net from sequence [i] based on digital (28, 24)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 28 and N(F) ≥ 25, using
(120−92, 120, 39)-Net in Base 2 — Upper bound on s
There is no (28, 120, 40)-net in base 2, because
- 8 times m-reduction [i] would yield (28, 112, 40)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2112, 40, S2, 3, 84), but
- the LP bound with quadratic polynomials shows that M ≥ 1 474612 307823 891046 502660 957498 507264 / 255 > 2112 [i]
- extracting embedded OOA [i] would yield OOA(2112, 40, S2, 3, 84), but