Best Known (43, 43+44, s)-Nets in Base 16
(43, 43+44, 257)-Net over F16 — Constructive and digital
Digital (43, 87, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(43,256) in PG(86,16)) for nets [i] based on digital (0, 44, 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
(43, 43+44, 304)-Net over F16 — Digital
Digital (43, 87, 304)-net over F16, using
(43, 43+44, 34862)-Net in Base 16 — Upper bound on s
There is no (43, 87, 34863)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 573 514557 102247 043484 571544 706571 449907 552654 679097 446691 861916 353020 625311 807929 473434 291879 087564 100766 > 1687 [i]