Best Known (47−28, 47, s)-Nets in Base 27
(47−28, 47, 108)-Net over F27 — Constructive and digital
Digital (19, 47, 108)-net over F27, using
- t-expansion [i] based on digital (18, 47, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(47−28, 47, 148)-Net over F27 — Digital
Digital (19, 47, 148)-net over F27, using
- t-expansion [i] based on digital (18, 47, 148)-net over F27, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
(47−28, 47, 172)-Net in Base 27 — Constructive
(19, 47, 172)-net in base 27, using
- 1 times m-reduction [i] based on (19, 48, 172)-net in base 27, using
- base change [i] based on digital (7, 36, 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, 36, 172)-net over F81, using
(47−28, 47, 190)-Net in Base 27
(19, 47, 190)-net in base 27, using
- 5 times m-reduction [i] based on (19, 52, 190)-net in base 27, using
- base change [i] based on digital (6, 39, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 39, 190)-net over F81, using
(47−28, 47, 14844)-Net in Base 27 — Upper bound on s
There is no (19, 47, 14845)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 18 802825 195929 752012 296646 200002 600716 679444 476148 055463 193733 059009 > 2747 [i]