Best Known (86−35, 86, s)-Nets in Base 27
(86−35, 86, 252)-Net over F27 — Constructive and digital
Digital (51, 86, 252)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 18, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (7, 24, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (9, 44, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (7, 18, 82)-net over F27, using
(86−35, 86, 408)-Net in Base 27 — Constructive
(51, 86, 408)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- (33, 68, 370)-net in base 27, using
- base change [i] based on digital (16, 51, 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, 51, 370)-net over F81, using
- digital (1, 18, 38)-net over F27, using
(86−35, 86, 2190)-Net over F27 — Digital
Digital (51, 86, 2190)-net over F27, using
(86−35, 86, 3960862)-Net in Base 27 — Upper bound on s
There is no (51, 86, 3960863)-net in base 27, because
- 1 times m-reduction [i] would yield (51, 85, 3960863)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 46 336314 698642 714595 824564 832742 944249 020091 641075 766501 136168 659857 412248 597165 568683 467235 098737 308335 462718 598001 062279 > 2785 [i]