Best Known (87−53, 87, s)-Nets in Base 27
(87−53, 87, 128)-Net over F27 — Constructive and digital
Digital (34, 87, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 30, 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 (4, 57, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 30, 64)-net over F27, using
(87−53, 87, 172)-Net in Base 27 — Constructive
(34, 87, 172)-net in base 27, using
- 21 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
(87−53, 87, 220)-Net over F27 — Digital
Digital (34, 87, 220)-net over F27, using
- t-expansion [i] based on digital (33, 87, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
(87−53, 87, 298)-Net in Base 27
(34, 87, 298)-net in base 27, using
- 1 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
(87−53, 87, 22007)-Net in Base 27 — Upper bound on s
There is no (34, 87, 22008)-net in base 27, because
- 1 times m-reduction [i] would yield (34, 86, 22008)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1252 294300 995562 511957 243091 066333 074245 904892 308169 475633 062587 387995 656382 020474 596370 072624 801170 091953 315555 873588 748753 > 2786 [i]