Best Known (30, 30+47, s)-Nets in Base 27
(30, 30+47, 116)-Net over F27 — Constructive and digital
Digital (30, 77, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 26, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 51, 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 (3, 26, 52)-net over F27, using
(30, 30+47, 172)-Net in Base 27 — Constructive
(30, 77, 172)-net in base 27, using
- 15 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 69, 172)-net over F81, using
(30, 30+47, 208)-Net over F27 — Digital
Digital (30, 77, 208)-net over F27, using
- t-expansion [i] based on digital (24, 77, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(30, 30+47, 244)-Net in Base 27
(30, 77, 244)-net in base 27, using
- 7 times m-reduction [i] based on (30, 84, 244)-net in base 27, using
- base change [i] based on digital (9, 63, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 63, 244)-net over F81, using
(30, 30+47, 19450)-Net in Base 27 — Upper bound on s
There is no (30, 77, 19451)-net in base 27, because
- 1 times m-reduction [i] would yield (30, 76, 19451)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 6 076556 096835 419195 392964 850998 628029 629608 635913 730030 848239 351955 388160 550325 746672 330734 712965 846068 012923 > 2776 [i]