Best Known (59, 59+51, s)-Nets in Base 27
(59, 59+51, 222)-Net over F27 — Constructive and digital
Digital (59, 110, 222)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 21, 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 (6, 31, 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, 58, 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, 21, 64)-net over F27, using
(59, 59+51, 370)-Net in Base 27 — Constructive
(59, 110, 370)-net in base 27, using
- 272 times duplication [i] based on (57, 108, 370)-net in base 27, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
(59, 59+51, 1081)-Net over F27 — Digital
Digital (59, 110, 1081)-net over F27, using
(59, 59+51, 681381)-Net in Base 27 — Upper bound on s
There is no (59, 110, 681382)-net in base 27, because
- 1 times m-reduction [i] would yield (59, 109, 681382)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 043904 975845 878471 662471 322005 344239 049210 370245 331493 450233 545329 331323 875987 233794 866311 815625 601559 943422 645955 821331 752487 901751 629981 150967 601813 014317 > 27109 [i]