Best Known (13, 13+19, s)-Nets in Base 27
(13, 13+19, 96)-Net over F27 — Constructive and digital
Digital (13, 32, 96)-net over F27, using
- t-expansion [i] based on digital (11, 32, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(13, 13+19, 136)-Net over F27 — Digital
Digital (13, 32, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(13, 13+19, 160)-Net in Base 27 — Constructive
(13, 32, 160)-net in base 27, using
- base change [i] based on digital (5, 24, 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
(13, 13+19, 167)-Net in Base 27
(13, 32, 167)-net in base 27, using
- base change [i] based on digital (5, 24, 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
(13, 13+19, 13579)-Net in Base 27 — Upper bound on s
There is no (13, 32, 13580)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 31, 13580)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 235 692441 218748 279266 488943 064546 308180 859577 > 2731 [i]