Best Known (26, 59, s)-Nets in Base 27
(26, 59, 140)-Net over F27 — Constructive and digital
Digital (26, 59, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 20, 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, 39, 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, 20, 64)-net over F27, using
(26, 59, 172)-Net in Base 27 — Constructive
(26, 59, 172)-net in base 27, using
- 17 times m-reduction [i] based on (26, 76, 172)-net in base 27, using
- base change [i] based on digital (7, 57, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 57, 172)-net over F81, using
(26, 59, 215)-Net over F27 — Digital
Digital (26, 59, 215)-net over F27, using
(26, 59, 244)-Net in Base 27
(26, 59, 244)-net in base 27, using
- 9 times m-reduction [i] based on (26, 68, 244)-net in base 27, using
- base change [i] based on digital (9, 51, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 51, 244)-net over F81, using
(26, 59, 40380)-Net in Base 27 — Upper bound on s
There is no (26, 59, 40381)-net in base 27, because
- 1 times m-reduction [i] would yield (26, 58, 40381)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 104516 141348 714537 154618 411104 672157 778071 225995 870716 367796 914160 858261 690015 654465 > 2758 [i]