Best Known (28, 28+35, s)-Nets in Base 27
(28, 28+35, 146)-Net over F27 — Constructive and digital
Digital (28, 63, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 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 (7, 42, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 21, 64)-net over F27, using
(28, 28+35, 172)-Net in Base 27 — Constructive
(28, 63, 172)-net in base 27, using
- 21 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 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, 63, 172)-net over F81, using
(28, 28+35, 234)-Net over F27 — Digital
Digital (28, 63, 234)-net over F27, using
(28, 28+35, 298)-Net in Base 27
(28, 63, 298)-net in base 27, using
- 1 times m-reduction [i] based on (28, 64, 298)-net in base 27, using
- base change [i] based on digital (12, 48, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 48, 298)-net over F81, using
(28, 28+35, 45830)-Net in Base 27 — Upper bound on s
There is no (28, 63, 45831)-net in base 27, because
- 1 times m-reduction [i] would yield (28, 62, 45831)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 55536 811152 949516 108520 565019 742682 957639 915742 730953 698593 092981 023362 255327 859738 180375 > 2762 [i]