Best Known (145−53, 145, s)-Nets in Base 2
(145−53, 145, 66)-Net over F2 — Constructive and digital
Digital (92, 145, 66)-net over F2, using
- 9 times m-reduction [i] based on digital (92, 154, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 77, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 77, 33)-net over F4, using
(145−53, 145, 87)-Net over F2 — Digital
Digital (92, 145, 87)-net over F2, using
(145−53, 145, 453)-Net in Base 2 — Upper bound on s
There is no (92, 145, 454)-net in base 2, because
- 1 times m-reduction [i] would yield (92, 144, 454)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 23 260845 255072 284096 306459 372654 791277 260400 > 2144 [i]