Best Known (79−51, 79, s)-Nets in Base 2
(79−51, 79, 21)-Net over F2 — Constructive and digital
Digital (28, 79, 21)-net over F2, using
- t-expansion [i] based on digital (21, 79, 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
(79−51, 79, 25)-Net over F2 — Digital
Digital (28, 79, 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
(79−51, 79, 57)-Net in Base 2 — Upper bound on s
There is no (28, 79, 58)-net in base 2, because
- 1 times m-reduction [i] would yield (28, 78, 58)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 374037 640402 985983 617649 > 278 [i]