Best Known (29, 65, s)-Nets in Base 27
(29, 65, 146)-Net over F27 — Constructive and digital
Digital (29, 65, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 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, 43, 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, 22, 64)-net over F27, using
(29, 65, 172)-Net in Base 27 — Constructive
(29, 65, 172)-net in base 27, using
- 23 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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, 66, 172)-net over F81, using
(29, 65, 244)-Net over F27 — Digital
Digital (29, 65, 244)-net over F27, using
(29, 65, 298)-Net in Base 27
(29, 65, 298)-net in base 27, using
- 3 times m-reduction [i] based on (29, 68, 298)-net in base 27, using
- base change [i] based on digital (12, 51, 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, 51, 298)-net over F81, using
(29, 65, 42842)-Net in Base 27 — Upper bound on s
There is no (29, 65, 42843)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1093 185780 454645 889921 172106 047229 115537 942950 754659 808021 434041 115500 213712 008137 760205 121029 > 2765 [i]