Best Known (41, 41+57, s)-Nets in Base 16
(41, 41+57, 225)-Net over F16 — Constructive and digital
Digital (41, 98, 225)-net over F16, using
- t-expansion [i] based on digital (40, 98, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
(41, 41+57, 11161)-Net in Base 16 — Upper bound on s
There is no (41, 98, 11162)-net in base 16, because
- 1 times m-reduction [i] would yield (41, 97, 11162)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 630 833261 098556 772803 888831 780144 479360 760228 984425 562978 114936 786061 126675 143329 995090 079494 510095 786480 428783 534816 > 1697 [i]