Best Known (33, 77, s)-Nets in Base 27
(33, 77, 146)-Net over F27 — Constructive and digital
Digital (33, 77, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 26, 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, 51, 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, 26, 64)-net over F27, using
(33, 77, 224)-Net in Base 27 — Constructive
(33, 77, 224)-net in base 27, using
- 3 times m-reduction [i] based on (33, 80, 224)-net in base 27, using
- base change [i] based on digital (13, 60, 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, 60, 224)-net over F81, using
(33, 77, 231)-Net over F27 — Digital
Digital (33, 77, 231)-net over F27, using
(33, 77, 298)-Net in Base 27
(33, 77, 298)-net in base 27, using
- 7 times m-reduction [i] based on (33, 84, 298)-net in base 27, using
- base change [i] based on digital (12, 63, 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, 63, 298)-net over F81, using
(33, 77, 35605)-Net in Base 27 — Upper bound on s
There is no (33, 77, 35606)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 164 134961 496681 782251 000104 575274 502780 321762 775941 797120 737540 186472 569957 637147 458608 756416 315322 201359 171477 > 2777 [i]