MinT - Best Known (145−119, 145, s)-Nets in Base 8

Best Known (145−119, 145, s)-Nets in Base 8

(145−119, 145, 65)-Net over F₈ — Constructive and digital

Digital (26, 145, 65)-net over F₈, using

t-expansion [i] based on digital (14, 145, 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]

(145−119, 145, 86)-Net over F₈ — Digital

Digital (26, 145, 86)-net over F₈, using

t-expansion [i] based on digital (25, 145, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(145−119, 145, 485)-Net in Base 8 — Upper bound on s

There is no (26, 145, 486)-net in base 8, because

1 times m-reduction [i] would yield (26, 144, 486)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12380 056794 718411 613243 124867 861453 831785 694715 081524 196912 557540 168787 032097 014849 610398 472109 548228 907820 061424 144413 648556 126032 > 8¹⁴⁴ [i]