Best Known (32, 32+45, s)-Nets in Base 27
(32, 32+45, 140)-Net over F27 — Constructive and digital
Digital (32, 77, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 26, 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, 51, 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, 26, 64)-net over F27, using
(32, 32+45, 172)-Net in Base 27 — Constructive
(32, 77, 172)-net in base 27, using
- 23 times m-reduction [i] based on (32, 100, 172)-net in base 27, using
- base change [i] based on digital (7, 75, 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, 75, 172)-net over F81, using
(32, 32+45, 208)-Net over F27 — Digital
Digital (32, 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
(32, 32+45, 298)-Net in Base 27
(32, 77, 298)-net in base 27, using
- 3 times m-reduction [i] based on (32, 80, 298)-net in base 27, using
- base change [i] based on digital (12, 60, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 60, 298)-net over F81, using
(32, 32+45, 30649)-Net in Base 27 — Upper bound on s
There is no (32, 77, 30650)-net in base 27, because
- 1 times m-reduction [i] would yield (32, 76, 30650)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 6 076500 871090 596389 230768 118826 913262 282637 360632 707876 387141 742842 967938 534061 369964 040330 923242 066117 155821 > 2776 [i]