Best Known (103−61, 103, s)-Nets in Base 27
(103−61, 103, 152)-Net over F27 — Constructive and digital
Digital (42, 103, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 36, 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, 67, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 36, 76)-net over F27, using
(103−61, 103, 280)-Net over F27 — Digital
Digital (42, 103, 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
(103−61, 103, 370)-Net in Base 27 — Constructive
(42, 103, 370)-net in base 27, using
- 1 times m-reduction [i] based on (42, 104, 370)-net in base 27, using
- base change [i] based on digital (16, 78, 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, 78, 370)-net over F81, using
(103−61, 103, 34060)-Net in Base 27 — Upper bound on s
There is no (42, 103, 34061)-net in base 27, because
- 1 times m-reduction [i] would yield (42, 102, 34061)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 99 827002 207900 811096 177855 047075 092172 761635 001245 183162 469349 035826 629078 316483 222575 316970 316038 183013 782630 532652 751458 765488 721666 127391 013921 > 27102 [i]