Best Known (62−41, 62, s)-Nets in Base 27
(62−41, 62, 108)-Net over F27 — Constructive and digital
Digital (21, 62, 108)-net over F27, using
- t-expansion [i] based on digital (18, 62, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(62−41, 62, 160)-Net in Base 27 — Constructive
(21, 62, 160)-net in base 27, using
- 2 times m-reduction [i] based on (21, 64, 160)-net in base 27, using
- base change [i] based on digital (5, 48, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 48, 160)-net over F81, using
(62−41, 62, 163)-Net over F27 — Digital
Digital (21, 62, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
(62−41, 62, 167)-Net in Base 27
(21, 62, 167)-net in base 27, using
- 2 times m-reduction [i] based on (21, 64, 167)-net in base 27, using
- base change [i] based on digital (5, 48, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- base change [i] based on digital (5, 48, 167)-net over F81, using
(62−41, 62, 7402)-Net in Base 27 — Upper bound on s
There is no (21, 62, 7403)-net in base 27, because
- 1 times m-reduction [i] would yield (21, 61, 7403)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2058 419909 461716 109468 579272 474459 628322 828836 569108 693662 124843 371322 736823 654079 790041 > 2761 [i]