Best Known (125−63, 125, s)-Nets in Base 16
(125−63, 125, 257)-Net over F16 — Constructive and digital
Digital (62, 125, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(62,256) in PG(124,16)) for nets [i] based on digital (0, 63, 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
(125−63, 125, 415)-Net over F16 — Digital
Digital (62, 125, 415)-net over F16, using
(125−63, 125, 54235)-Net in Base 16 — Upper bound on s
There is no (62, 125, 54236)-net in base 16, because
- 1 times m-reduction [i] would yield (62, 124, 54236)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 204625 603741 591700 264872 984957 735068 501958 606921 680947 942356 330355 940555 317288 076808 311267 327059 598696 413244 352346 254015 689649 790512 830195 338058 045616 > 16124 [i]