Best Known (21, 21+34, s)-Nets in Base 27
(21, 21+34, 108)-Net over F27 — Constructive and digital
Digital (21, 55, 108)-net over F27, using
- t-expansion [i] based on digital (18, 55, 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
(21, 21+34, 163)-Net over F27 — Digital
Digital (21, 55, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
(21, 21+34, 172)-Net in Base 27 — Constructive
(21, 55, 172)-net in base 27, using
- 1 times m-reduction [i] based on (21, 56, 172)-net in base 27, using
- base change [i] based on digital (7, 42, 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, 42, 172)-net over F81, using
(21, 21+34, 190)-Net in Base 27
(21, 55, 190)-net in base 27, using
- 5 times m-reduction [i] based on (21, 60, 190)-net in base 27, using
- base change [i] based on digital (6, 45, 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, 45, 190)-net over F81, using
(21, 21+34, 11790)-Net in Base 27 — Upper bound on s
There is no (21, 55, 11791)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 5 311962 691751 269587 334928 932975 155782 835573 995514 756117 673516 356313 617640 041447 > 2755 [i]