Best Known (6, 6+15, s)-Nets in Base 27
(6, 6+15, 76)-Net over F27 — Constructive and digital
Digital (6, 21, 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
(6, 6+15, 82)-Net in Base 27 — Constructive
(6, 21, 82)-net in base 27, using
- 3 times m-reduction [i] based on (6, 24, 82)-net in base 27, using
- base change [i] based on digital (0, 18, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- base change [i] based on digital (0, 18, 82)-net over F81, using
(6, 6+15, 1594)-Net in Base 27 — Upper bound on s
There is no (6, 21, 1595)-net in base 27, because
- 1 times m-reduction [i] would yield (6, 20, 1595)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 42455 024202 325851 434564 034075 > 2720 [i]