MinT - Best Known (152−117, 152, s)-Nets in Base 8

Best Known (152−117, 152, s)-Nets in Base 8

(152−117, 152, 65)-Net over F₈ — Constructive and digital

Digital (35, 152, 65)-net over F₈, using

t-expansion [i] based on digital (14, 152, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(152−117, 152, 112)-Net over F₈ — Digital

Digital (35, 152, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(152−117, 152, 683)-Net in Base 8 — Upper bound on s

There is no (35, 152, 684)-net in base 8, because

1 times m-reduction [i] would yield (35, 151, 684)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23866 477210 526517 280256 446500 711839 338854 373292 388005 834798 702829 687921 174815 032867 711954 775906 359570 692762 620338 782184 749419 972747 516840 > 8¹⁵¹ [i]