MinT - Best Known (162−129, 162, s)-Nets in Base 8

Best Known (162−129, 162, s)-Nets in Base 8

(162−129, 162, 65)-Net over F₈ — Constructive and digital

Digital (33, 162, 65)-net over F₈, using

t-expansion [i] based on digital (14, 162, 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]

(162−129, 162, 97)-Net over F₈ — Digital

Digital (33, 162, 97)-net over F₈, using

t-expansion [i] based on digital (28, 162, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(162−129, 162, 619)-Net in Base 8 — Upper bound on s

There is no (33, 162, 620)-net in base 8, because

1 times m-reduction [i] would yield (33, 161, 620)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26 893647 878505 162674 114919 990060 610962 707987 234571 396939 333483 506632 800768 811040 526549 311385 143566 991825 842124 133191 557421 044243 984373 287817 487327 > 8¹⁶¹ [i]