Best Known (110−55, 110, s)-Nets in Base 16
(110−55, 110, 514)-Net over F16 — Constructive and digital
Digital (55, 110, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 55, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(110−55, 110, 52877)-Net in Base 16 — Upper bound on s
There is no (55, 110, 52878)-net in base 16, because
- 1 times m-reduction [i] would yield (55, 109, 52878)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 177495 782212 925942 145383 215108 480072 502525 562357 916071 270741 792980 730051 969966 095371 067692 275758 177767 882297 947581 857235 284243 348816 > 16109 [i]