Best Known (36, 36+45, s)-Nets in Base 27
(36, 36+45, 164)-Net over F27 — Constructive and digital
Digital (36, 81, 164)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 29, 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 (7, 52, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (7, 29, 82)-net over F27, using
(36, 36+45, 224)-Net in Base 27 — Constructive
(36, 81, 224)-net in base 27, using
- 11 times m-reduction [i] based on (36, 92, 224)-net in base 27, using
- base change [i] based on digital (13, 69, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 69, 224)-net over F81, using
(36, 36+45, 282)-Net over F27 — Digital
Digital (36, 81, 282)-net over F27, using
(36, 36+45, 298)-Net in Base 27
(36, 81, 298)-net in base 27, using
- 15 times m-reduction [i] based on (36, 96, 298)-net in base 27, using
- base change [i] based on digital (12, 72, 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, 72, 298)-net over F81, using
(36, 36+45, 55814)-Net in Base 27 — Upper bound on s
There is no (36, 81, 55815)-net in base 27, because
- 1 times m-reduction [i] would yield (36, 80, 55815)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3 229307 962875 872192 481942 605063 389539 336712 021147 535019 474786 316709 795068 997015 068964 108303 207605 217053 852882 885269 > 2780 [i]