Best Known (39, 39+40, s)-Nets in Base 16
(39, 39+40, 257)-Net over F16 — Constructive and digital
Digital (39, 79, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(39,256) in PG(78,16)) for nets [i] based on digital (0, 40, 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
(39, 39+40, 281)-Net over F16 — Digital
Digital (39, 79, 281)-net over F16, using
(39, 39+40, 31574)-Net in Base 16 — Upper bound on s
There is no (39, 79, 31575)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 133520 235763 285540 798485 906838 359578 008419 514217 490470 674294 770767 613861 101958 701737 069518 716251 > 1679 [i]