Best Known (79−45, 79, s)-Nets in Base 27
(79−45, 79, 152)-Net over F27 — Constructive and digital
Digital (34, 79, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 28, 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 (6, 51, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 28, 76)-net over F27, using
(79−45, 79, 224)-Net in Base 27 — Constructive
(34, 79, 224)-net in base 27, using
- 5 times m-reduction [i] based on (34, 84, 224)-net in base 27, using
- base change [i] based on digital (13, 63, 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, 63, 224)-net over F81, using
(79−45, 79, 240)-Net over F27 — Digital
Digital (34, 79, 240)-net over F27, using
(79−45, 79, 298)-Net in Base 27
(34, 79, 298)-net in base 27, using
- 9 times m-reduction [i] based on (34, 88, 298)-net in base 27, using
- base change [i] based on digital (12, 66, 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, 66, 298)-net over F81, using
(79−45, 79, 41361)-Net in Base 27 — Upper bound on s
There is no (34, 79, 41362)-net in base 27, because
- 1 times m-reduction [i] would yield (34, 78, 41362)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 4430 993653 768871 266584 386021 061436 774795 001642 680965 047293 512936 487879 039520 754409 727083 753105 349014 204589 301117 > 2778 [i]