Best Known (28−19, 28, s)-Nets in Base 27
(28−19, 28, 88)-Net over F27 — Constructive and digital
Digital (9, 28, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
(28−19, 28, 99)-Net over F27 — Digital
Digital (9, 28, 99)-net over F27, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 99, using
(28−19, 28, 116)-Net in Base 27 — Constructive
(9, 28, 116)-net in base 27, using
- base change [i] based on digital (2, 21, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
(28−19, 28, 118)-Net in Base 27
(9, 28, 118)-net in base 27, using
- base change [i] based on digital (2, 21, 118)-net over F81, using
- net from sequence [i] based on digital (2, 117)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 118, using
- net from sequence [i] based on digital (2, 117)-sequence over F81, using
(28−19, 28, 3135)-Net in Base 27 — Upper bound on s
There is no (9, 28, 3136)-net in base 27, because
- 1 times m-reduction [i] would yield (9, 27, 3136)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 444 419296 035134 965972 276696 018412 659329 > 2727 [i]