Best Known (4, 9, s)-Nets in Base 16
(4, 9, 257)-Net over F16 — Constructive and digital
Digital (4, 9, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(4,256) in PG(8,16)) for nets [i] based on digital (0, 5, 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
(4, 9, 496)-Net in Base 16 — Constructive
(4, 9, 496)-net in base 16, using
- net defined by OOA [i] based on OOA(169, 496, S16, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(169, 993, S16, 5), using
- discarding parts of the base [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(169, 993, S16, 5), using
(4, 9, 6178)-Net in Base 16 — Upper bound on s
There is no (4, 9, 6179)-net in base 16, because
- 1 times m-reduction [i] would yield (4, 8, 6179)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 4296 135121 > 168 [i]