Best Known (52−31, 52, s)-Nets in Base 27
(52−31, 52, 112)-Net over F27 — Constructive and digital
Digital (21, 52, 112)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 17, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (4, 35, 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 (2, 17, 48)-net over F27, using
(52−31, 52, 163)-Net over F27 — Digital
Digital (21, 52, 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
(52−31, 52, 172)-Net in Base 27 — Constructive
(21, 52, 172)-net in base 27, using
- 4 times m-reduction [i] based on (21, 56, 172)-net in base 27, using
- base change [i] based on digital (7, 42, 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, 42, 172)-net over F81, using
(52−31, 52, 226)-Net in Base 27
(21, 52, 226)-net in base 27, using
- base change [i] based on digital (8, 39, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
(52−31, 52, 18165)-Net in Base 27 — Upper bound on s
There is no (21, 52, 18166)-net in base 27, because
- 1 times m-reduction [i] would yield (21, 51, 18166)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 9 993245 230045 940019 992198 640664 061746 359834 300022 182410 256399 939216 351513 > 2751 [i]