Best Known (70, 70+39, s)-Nets in Base 27
(70, 70+39, 332)-Net over F27 — Constructive and digital
Digital (70, 109, 332)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 11, 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, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 17, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 23, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (6, 45, 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 (4, 11, 64)-net over F27, using
(70, 70+39, 730)-Net in Base 27 — Constructive
(70, 109, 730)-net in base 27, using
- 271 times duplication [i] based on (69, 108, 730)-net in base 27, using
- t-expansion [i] based on (63, 108, 730)-net in base 27, using
- base change [i] based on digital (36, 81, 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
- base change [i] based on digital (36, 81, 730)-net over F81, using
- t-expansion [i] based on (63, 108, 730)-net in base 27, using
(70, 70+39, 7391)-Net over F27 — Digital
Digital (70, 109, 7391)-net over F27, using
(70, 70+39, large)-Net in Base 27 — Upper bound on s
There is no (70, 109, large)-net in base 27, because
- 37 times m-reduction [i] would yield (70, 72, large)-net in base 27, but