Best Known (253−117, 253, s)-Nets in Base 2
(253−117, 253, 66)-Net over F2 — Constructive and digital
Digital (136, 253, 66)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 97, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (39, 156, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2 (see above)
- digital (39, 97, 33)-net over F2, using
(253−117, 253, 81)-Net over F2 — Digital
Digital (136, 253, 81)-net over F2, using
- t-expansion [i] based on digital (126, 253, 81)-net over F2, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
(253−117, 253, 376)-Net in Base 2 — Upper bound on s
There is no (136, 253, 377)-net in base 2, because
- 1 times m-reduction [i] would yield (136, 252, 377)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7716 767071 196823 680360 653430 870097 900985 149792 182902 052997 219359 400422 833020 > 2252 [i]