Best Known (82−49, 82, s)-Nets in Base 2
(82−49, 82, 24)-Net over F2 — Constructive and digital
Digital (33, 82, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
(82−49, 82, 28)-Net over F2 — Digital
Digital (33, 82, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(82−49, 82, 70)-Net in Base 2 — Upper bound on s
There is no (33, 82, 71)-net in base 2, because
- 1 times m-reduction [i] would yield (33, 81, 71)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 428808 452728 863612 591576 > 281 [i]