Best Known (165−56, 165, s)-Nets in Base 8
(165−56, 165, 402)-Net over F8 — Constructive and digital
Digital (109, 165, 402)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 39, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- digital (70, 126, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 63, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 63, 177)-net over F64, using
- digital (11, 39, 48)-net over F8, using
(165−56, 165, 576)-Net in Base 8 — Constructive
(109, 165, 576)-net in base 8, using
- t-expansion [i] based on (108, 165, 576)-net in base 8, using
- 7 times m-reduction [i] based on (108, 172, 576)-net in base 8, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
- 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
- 7 times m-reduction [i] based on (108, 172, 576)-net in base 8, using
(165−56, 165, 1588)-Net over F8 — Digital
Digital (109, 165, 1588)-net over F8, using
(165−56, 165, 338582)-Net in Base 8 — Upper bound on s
There is no (109, 165, 338583)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 102295 599149 675197 880610 824042 353889 822923 248310 145138 577455 703358 101163 342794 349601 328558 242078 520061 337177 436341 688290 352487 414283 328144 571785 720464 > 8165 [i]