Best Known (42, 42+68, s)-Nets in Base 27
(42, 42+68, 128)-Net over F27 — Constructive and digital
Digital (42, 110, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 38, 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 (4, 72, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 38, 64)-net over F27, using
(42, 42+68, 224)-Net in Base 27 — Constructive
(42, 110, 224)-net in base 27, using
- 272 times duplication [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 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, 81, 224)-net over F81, using
(42, 42+68, 280)-Net over F27 — Digital
Digital (42, 110, 280)-net over F27, using
- net from sequence [i] based on digital (42, 279)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 42 and N(F) ≥ 280, using
(42, 42+68, 298)-Net in Base 27
(42, 110, 298)-net in base 27, using
- 272 times duplication [i] based on (40, 108, 298)-net in base 27, using
- t-expansion [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 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, 81, 298)-net over F81, using
- t-expansion [i] based on (39, 108, 298)-net in base 27, using
(42, 42+68, 22235)-Net in Base 27 — Upper bound on s
There is no (42, 110, 22236)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 28 227626 977523 102377 094907 267275 942647 083774 881078 532996 951008 425013 498473 101992 834808 209562 392632 230380 009124 535408 861584 141457 625112 010660 719725 124665 148489 > 27110 [i]