Best Known (53, 91, s)-Nets in Base 27
(53, 91, 248)-Net over F27 — Constructive and digital
Digital (53, 91, 248)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 19, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (7, 26, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (8, 46, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 19, 82)-net over F27, using
(53, 91, 398)-Net in Base 27 — Constructive
(53, 91, 398)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (0, 19, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- (34, 72, 370)-net in base 27, using
- base change [i] based on digital (16, 54, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 54, 370)-net over F81, using
- digital (0, 19, 28)-net over F27, using
(53, 91, 1886)-Net over F27 — Digital
Digital (53, 91, 1886)-net over F27, using
(53, 91, 2186348)-Net in Base 27 — Upper bound on s
There is no (53, 91, 2186349)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 17951 716924 332675 957822 381906 222556 631422 796912 570863 793179 212523 938016 087476 922551 292482 723792 319729 978446 878174 963228 552048 377267 > 2791 [i]