Best Known (65−41, 65, s)-Nets in Base 27
(65−41, 65, 114)-Net over F27 — Constructive and digital
Digital (24, 65, 114)-net over F27, using
- t-expansion [i] based on digital (23, 65, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(65−41, 65, 172)-Net in Base 27 — Constructive
(24, 65, 172)-net in base 27, using
- 3 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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, 51, 172)-net over F81, using
(65−41, 65, 208)-Net over F27 — Digital
Digital (24, 65, 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
(65−41, 65, 12143)-Net in Base 27 — Upper bound on s
There is no (24, 65, 12144)-net in base 27, because
- 1 times m-reduction [i] would yield (24, 64, 12144)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 40 543194 390266 907353 583420 257992 393340 717646 188220 708083 840417 105539 727210 467723 426428 625537 > 2764 [i]