Best Known (100−56, 100, s)-Nets in Base 27
(100−56, 100, 170)-Net over F27 — Constructive and digital
Digital (44, 100, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (9, 65, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (7, 35, 82)-net over F27, using
(100−56, 100, 319)-Net over F27 — Digital
Digital (44, 100, 319)-net over F27, using
(100−56, 100, 370)-Net in Base 27 — Constructive
(44, 100, 370)-net in base 27, using
- t-expansion [i] based on (43, 100, 370)-net in base 27, using
- 8 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- 8 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(100−56, 100, 56225)-Net in Base 27 — Upper bound on s
There is no (44, 100, 56226)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 136932 398640 884303 008581 594636 893769 743495 329486 833338 696917 550477 859418 297217 743738 076994 169155 655921 472137 459085 780036 525950 301856 510773 896473 > 27100 [i]