Best Known (173−61, 173, s)-Nets in Base 8
(173−61, 173, 388)-Net over F8 — Constructive and digital
Digital (112, 173, 388)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 37, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (75, 136, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 68, 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, 68, 177)-net over F64, using
- digital (7, 37, 34)-net over F8, using
(173−61, 173, 576)-Net in Base 8 — Constructive
(112, 173, 576)-net in base 8, using
- 81 times duplication [i] based on (111, 172, 576)-net in base 8, using
- t-expansion [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
- t-expansion [i] based on (108, 172, 576)-net in base 8, using
(173−61, 173, 1361)-Net over F8 — Digital
Digital (112, 173, 1361)-net over F8, using
(173−61, 173, 259044)-Net in Base 8 — Upper bound on s
There is no (112, 173, 259045)-net in base 8, because
- 1 times m-reduction [i] would yield (112, 172, 259045)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 214527 184314 863794 069763 407090 019998 885018 389148 191551 897771 315385 505564 482507 836977 381027 351799 942830 945480 586463 880931 053943 110674 556142 667446 153115 312560 > 8172 [i]