Best Known (16, 16+23, s)-Nets in Base 27
(16, 16+23, 102)-Net over F27 — Constructive and digital
Digital (16, 39, 102)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (4, 27, 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 (1, 12, 38)-net over F27, using
(16, 16+23, 144)-Net over F27 — Digital
Digital (16, 39, 144)-net over F27, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
(16, 16+23, 160)-Net in Base 27 — Constructive
(16, 39, 160)-net in base 27, using
- 5 times m-reduction [i] based on (16, 44, 160)-net in base 27, using
- base change [i] based on digital (5, 33, 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, 33, 160)-net over F81, using
(16, 16+23, 190)-Net in Base 27
(16, 39, 190)-net in base 27, using
- 1 times m-reduction [i] based on (16, 40, 190)-net in base 27, using
- base change [i] based on digital (6, 30, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 30, 190)-net over F81, using
(16, 16+23, 16619)-Net in Base 27 — Upper bound on s
There is no (16, 39, 16620)-net in base 27, because
- 1 times m-reduction [i] would yield (16, 38, 16620)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2 466327 524674 496636 767894 075152 339153 955863 006566 028209 > 2738 [i]