Best Known (169−60, 169, s)-Nets in Base 8
(169−60, 169, 382)-Net over F8 — Constructive and digital
Digital (109, 169, 382)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 35, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (74, 134, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 67, 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, 67, 177)-net over F64, using
- digital (5, 35, 28)-net over F8, using
(169−60, 169, 576)-Net in Base 8 — Constructive
(109, 169, 576)-net in base 8, using
- t-expansion [i] based on (108, 169, 576)-net in base 8, using
- 3 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
- 3 times m-reduction [i] based on (108, 172, 576)-net in base 8, using
(169−60, 169, 1289)-Net over F8 — Digital
Digital (109, 169, 1289)-net over F8, using
(169−60, 169, 210406)-Net in Base 8 — Upper bound on s
There is no (109, 169, 210407)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 419 034535 690183 811134 117887 211713 225254 196003 750869 015380 566669 691980 129065 495648 938928 773188 333132 419230 641601 545041 332459 573541 180246 408514 150599 455020 > 8169 [i]