Best Known (13, 13+17, s)-Nets in Base 27
(13, 13+17, 102)-Net over F27 — Constructive and digital
Digital (13, 30, 102)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 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, 21, 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, 9, 38)-net over F27, using
(13, 13+17, 136)-Net over F27 — Digital
Digital (13, 30, 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+17, 160)-Net in Base 27 — Constructive
(13, 30, 160)-net in base 27, using
- 2 times m-reduction [i] based on (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
- base change [i] based on digital (5, 24, 160)-net over F81, using
(13, 13+17, 167)-Net in Base 27
(13, 30, 167)-net in base 27, using
- 2 times m-reduction [i] based on (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
- base change [i] based on digital (5, 24, 167)-net over F81, using
(13, 13+17, 22353)-Net in Base 27 — Upper bound on s
There is no (13, 30, 22354)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 29, 22354)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 323370 177303 235488 710777 308349 246458 425681 > 2729 [i]