Best Known (63−36, 63, s)-Nets in Base 27
(63−36, 63, 132)-Net over F27 — Constructive and digital
Digital (27, 63, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 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 (5, 41, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 22, 64)-net over F27, using
(63−36, 63, 172)-Net in Base 27 — Constructive
(27, 63, 172)-net in base 27, using
- 17 times m-reduction [i] based on (27, 80, 172)-net in base 27, using
- base change [i] based on digital (7, 60, 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, 60, 172)-net over F81, using
(63−36, 63, 208)-Net over F27 — Digital
Digital (27, 63, 208)-net over F27, using
- t-expansion [i] based on digital (24, 63, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(63−36, 63, 244)-Net in Base 27
(27, 63, 244)-net in base 27, using
- 9 times m-reduction [i] based on (27, 72, 244)-net in base 27, using
- base change [i] based on digital (9, 54, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 54, 244)-net over F81, using
(63−36, 63, 29702)-Net in Base 27 — Upper bound on s
There is no (27, 63, 29703)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 499697 341237 889436 741440 539329 025448 362585 059738 039006 734496 304004 936107 918396 409223 200189 > 2763 [i]