Best Known (60, 60+36, s)-Nets in Base 27
(60, 60+36, 286)-Net over F27 — Constructive and digital
Digital (60, 96, 286)-net over F27, using
- 1 times m-reduction [i] based on digital (60, 97, 286)-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 (7, 44, 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 (4, 13, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(60, 60+36, 730)-Net in Base 27 — Constructive
(60, 96, 730)-net in base 27, using
- base change [i] based on digital (36, 72, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
(60, 60+36, 4529)-Net over F27 — Digital
Digital (60, 96, 4529)-net over F27, using
(60, 60+36, large)-Net in Base 27 — Upper bound on s
There is no (60, 96, large)-net in base 27, because
- 34 times m-reduction [i] would yield (60, 62, large)-net in base 27, but