Best Known (65−27, 65, s)-Nets in Base 27
(65−27, 65, 216)-Net over F27 — Constructive and digital
Digital (38, 65, 216)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (6, 19, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 33, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (4, 13, 64)-net over F27, using
(65−27, 65, 370)-Net in Base 27 — Constructive
(38, 65, 370)-net in base 27, using
- 23 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
- base change [i] based on digital (16, 66, 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, 66, 370)-net over F81, using
(65−27, 65, 1550)-Net over F27 — Digital
Digital (38, 65, 1550)-net over F27, using
(65−27, 65, 2427423)-Net in Base 27 — Upper bound on s
There is no (38, 65, 2427424)-net in base 27, because
- 1 times m-reduction [i] would yield (38, 64, 2427424)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 40 483836 741265 381097 101711 580455 514446 461913 744374 304413 271944 791704 682835 563455 982900 309313 > 2764 [i]