Best Known (57, 90, s)-Nets in Base 27
(57, 90, 292)-Net over F27 — Constructive and digital
Digital (57, 90, 292)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 12, 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, 17, 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, 22, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 39, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (4, 12, 64)-net over F27, using
(57, 90, 486)-Net in Base 27 — Constructive
(57, 90, 486)-net in base 27, using
- (u, u+v)-construction [i] based on
- (8, 24, 116)-net in base 27, using
- base change [i] based on digital (2, 18, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 18, 116)-net over F81, using
- (33, 66, 370)-net in base 27, using
- 2 times m-reduction [i] based on (33, 68, 370)-net in base 27, using
- base change [i] based on digital (16, 51, 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, 51, 370)-net over F81, using
- 2 times m-reduction [i] based on (33, 68, 370)-net in base 27, using
- (8, 24, 116)-net in base 27, using
(57, 90, 5235)-Net over F27 — Digital
Digital (57, 90, 5235)-net over F27, using
(57, 90, large)-Net in Base 27 — Upper bound on s
There is no (57, 90, large)-net in base 27, because
- 31 times m-reduction [i] would yield (57, 59, large)-net in base 27, but