Best Known (21, 21+33, s)-Nets in Base 27
(21, 21+33, 108)-Net over F27 — Constructive and digital
Digital (21, 54, 108)-net over F27, using
- t-expansion [i] based on digital (18, 54, 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+33, 163)-Net over F27 — Digital
Digital (21, 54, 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+33, 172)-Net in Base 27 — Constructive
(21, 54, 172)-net in base 27, using
- 2 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+33, 190)-Net in Base 27
(21, 54, 190)-net in base 27, using
- 6 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+33, 14411)-Net in Base 27 — Upper bound on s
There is no (21, 54, 14412)-net in base 27, because
- 1 times m-reduction [i] would yield (21, 53, 14412)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 7285 397058 458889 362187 085818 374118 119623 675740 889667 875839 832404 336205 094529 > 2753 [i]