Best Known (43, 110, s)-Nets in Base 27
(43, 110, 140)-Net over F27 — Constructive and digital
Digital (43, 110, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 37, 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, 73, 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 (4, 37, 64)-net over F27, using
(43, 110, 224)-Net in Base 27 — Constructive
(43, 110, 224)-net in base 27, using
- 272 times duplication [i] based on (41, 108, 224)-net in base 27, using
- t-expansion [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
- t-expansion [i] based on (40, 108, 224)-net in base 27, using
(43, 110, 280)-Net over F27 — Digital
Digital (43, 110, 280)-net over F27, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (42, 279)-sequence over F27, using
(43, 110, 298)-Net in Base 27
(43, 110, 298)-net in base 27, using
- 272 times duplication [i] based on (41, 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
(43, 110, 27035)-Net in Base 27 — Upper bound on s
There is no (43, 110, 27036)-net in base 27, because
- 1 times m-reduction [i] would yield (43, 109, 27036)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 043963 697413 518992 347909 002206 829157 937458 683364 727112 196507 386208 750500 045731 939798 285773 774239 370384 652320 210303 727386 864081 040775 006712 646349 224119 150041 > 27109 [i]