Best Known (65−28, 65, s)-Nets in Base 27
(65−28, 65, 204)-Net over F27 — Constructive and digital
Digital (37, 65, 204)-net over F27, using
- 1 times m-reduction [i] based on digital (37, 66, 204)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 13, 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, 18, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (6, 35, 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
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 13, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(65−28, 65, 370)-Net in Base 27 — Constructive
(37, 65, 370)-net in base 27, using
- 19 times m-reduction [i] based on (37, 84, 370)-net in base 27, using
- base change [i] based on digital (16, 63, 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, 63, 370)-net over F81, using
(65−28, 65, 1187)-Net over F27 — Digital
Digital (37, 65, 1187)-net over F27, using
(65−28, 65, 1028250)-Net in Base 27 — Upper bound on s
There is no (37, 65, 1028251)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1093 070329 413538 691829 748133 667159 268213 813576 680199 799920 049186 772199 691785 697322 114564 656109 > 2765 [i]