Best Known (42, 85, s)-Nets in Base 16
(42, 85, 257)-Net over F16 — Constructive and digital
Digital (42, 85, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(42,256) in PG(84,16)) for nets [i] based on digital (0, 43, 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
(42, 85, 298)-Net over F16 — Digital
Digital (42, 85, 298)-net over F16, using
(42, 85, 37909)-Net in Base 16 — Upper bound on s
There is no (42, 85, 37910)-net in base 16, because
- 1 times m-reduction [i] would yield (42, 84, 37910)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 140005 123502 975948 733533 729016 857223 053827 815193 820224 019983 099678 151061 466330 752339 782047 395042 309151 > 1684 [i]