MinT - Best Known (145−110, 145, s)-Nets in Base 8

Best Known (145−110, 145, s)-Nets in Base 8

(145−110, 145, 65)-Net over F₈ — Constructive and digital

Digital (35, 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]

(145−110, 145, 112)-Net over F₈ — Digital

Digital (35, 145, 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]

(145−110, 145, 698)-Net in Base 8 — Upper bound on s

There is no (35, 145, 699)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 93176 600664 699829 957296 877249 537722 863771 805473 236986 575052 404537 072367 983996 325911 670867 653664 127598 153367 966014 451013 963739 691752 > 8¹⁴⁵ [i]