Best Known (59−35, 59, s)-Nets in Base 27
(59−35, 59, 116)-Net over F27 — Constructive and digital
Digital (24, 59, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 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, 39, 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, 20, 52)-net over F27, using
(59−35, 59, 172)-Net in Base 27 — Constructive
(24, 59, 172)-net in base 27, using
- 9 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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, 51, 172)-net over F81, using
(59−35, 59, 208)-Net over F27 — Digital
Digital (24, 59, 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
(59−35, 59, 244)-Net in Base 27
(24, 59, 244)-net in base 27, using
- 1 times m-reduction [i] based on (24, 60, 244)-net in base 27, using
- base change [i] based on digital (9, 45, 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, 45, 244)-net over F81, using
(59−35, 59, 21099)-Net in Base 27 — Upper bound on s
There is no (24, 59, 21100)-net in base 27, because
- 1 times m-reduction [i] would yield (24, 58, 21100)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 104545 961040 700667 281302 382320 542649 588220 989525 782159 827771 936589 902350 563394 681081 > 2758 [i]