Best Known (105−65, 105, s)-Nets in Base 16
(105−65, 105, 225)-Net over F16 — Constructive and digital
Digital (40, 105, 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
(105−65, 105, 6967)-Net in Base 16 — Upper bound on s
There is no (40, 105, 6968)-net in base 16, because
- 1 times m-reduction [i] would yield (40, 104, 6968)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 169555 365890 013620 835972 024832 326827 902676 557149 952055 222354 190407 056683 399483 997228 546271 053404 058633 238045 796014 512989 816991 > 16104 [i]