Best Known (62−25, 62, s)-Nets in Base 27
(62−25, 62, 222)-Net over F27 — Constructive and digital
Digital (37, 62, 222)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 12, 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 (6, 18, 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 (7, 32, 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 (4, 12, 64)-net over F27, using
(62−25, 62, 370)-Net in Base 27 — Constructive
(37, 62, 370)-net in base 27, using
- 22 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
(62−25, 62, 1892)-Net over F27 — Digital
Digital (37, 62, 1892)-net over F27, using
(62−25, 62, 3841373)-Net in Base 27 — Upper bound on s
There is no (37, 62, 3841374)-net in base 27, because
- 1 times m-reduction [i] would yield (37, 61, 3841374)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2056 792169 856362 598036 746563 806322 464215 032623 293014 286083 269791 919060 642307 243022 665689 > 2761 [i]