Best Known (167−62, 167, s)-Nets in Base 8
(167−62, 167, 354)-Net over F8 — Constructive and digital
Digital (105, 167, 354)-net over F8, using
- t-expansion [i] based on digital (93, 167, 354)-net over F8, using
- 5 times m-reduction [i] based on digital (93, 172, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 86, 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, 86, 177)-net over F64, using
- 5 times m-reduction [i] based on digital (93, 172, 354)-net over F8, using
(167−62, 167, 576)-Net in Base 8 — Constructive
(105, 167, 576)-net in base 8, using
- 1 times m-reduction [i] based on (105, 168, 576)-net in base 8, using
- trace code for nets [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
- trace code for nets [i] based on (21, 84, 288)-net in base 64, using
(167−62, 167, 1011)-Net over F8 — Digital
Digital (105, 167, 1011)-net over F8, using
(167−62, 167, 129987)-Net in Base 8 — Upper bound on s
There is no (105, 167, 129988)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 6 546823 015837 336950 701449 562205 176841 685522 617577 729117 363481 475352 488533 530137 330661 337553 381653 135228 964917 391232 998224 411565 323959 931794 690283 915824 > 8167 [i]