Best Known (36, 36+46, s)-Nets in Base 27
(36, 36+46, 158)-Net over F27 — Constructive and digital
Digital (36, 82, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 29, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 53, 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 (6, 29, 76)-net over F27, using
(36, 36+46, 224)-Net in Base 27 — Constructive
(36, 82, 224)-net in base 27, using
- 10 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+46, 269)-Net over F27 — Digital
Digital (36, 82, 269)-net over F27, using
(36, 36+46, 298)-Net in Base 27
(36, 82, 298)-net in base 27, using
- 14 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+46, 45972)-Net in Base 27 — Upper bound on s
There is no (36, 82, 45973)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2355 264837 763695 808222 631694 527837 768306 110790 861688 374574 291827 433839 892794 788949 925584 585976 601406 548715 075482 540323 > 2782 [i]