Best Known (59, 59+37, s)-Nets in Base 27
(59, 59+37, 280)-Net over F27 — Constructive and digital
Digital (59, 96, 280)-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 (4, 16, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (6, 24, 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, 43, 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
(59, 59+37, 470)-Net in Base 27 — Constructive
(59, 96, 470)-net in base 27, using
- base change [i] based on digital (35, 72, 470)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 19, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (16, 53, 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
- digital (1, 19, 100)-net over F81, using
- (u, u+v)-construction [i] based on
(59, 59+37, 3622)-Net over F27 — Digital
Digital (59, 96, 3622)-net over F27, using
(59, 59+37, large)-Net in Base 27 — Upper bound on s
There is no (59, 96, large)-net in base 27, because
- 35 times m-reduction [i] would yield (59, 61, large)-net in base 27, but