Best Known (82−44, 82, s)-Nets in Base 27
(82−44, 82, 170)-Net over F27 — Constructive and digital
Digital (38, 82, 170)-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 (9, 53, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (7, 29, 82)-net over F27, using
(82−44, 82, 349)-Net over F27 — Digital
Digital (38, 82, 349)-net over F27, using
(82−44, 82, 370)-Net in Base 27 — Constructive
(38, 82, 370)-net in base 27, using
- 6 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
- base change [i] based on digital (16, 66, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 66, 370)-net over F81, using
(82−44, 82, 75317)-Net in Base 27 — Upper bound on s
There is no (38, 82, 75318)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2354 286791 727264 713980 353759 505406 234038 647941 179857 308585 467678 689311 368213 199104 868712 884099 154182 615425 500300 210261 > 2782 [i]