MinT - Best Known (112−62, 112, s)-Nets in Base 8

Best Known (112−62, 112, s)-Nets in Base 8

(112−62, 112, 98)-Net over F₈ — Constructive and digital

Digital (50, 112, 98)-net over F₈, using

t-expansion [i] based on digital (37, 112, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(112−62, 112, 144)-Net over F₈ — Digital

Digital (50, 112, 144)-net over F₈, using

t-expansion [i] based on digital (45, 112, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(112−62, 112, 3229)-Net in Base 8 — Upper bound on s

There is no (50, 112, 3230)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 140892 174793 439486 421201 356038 697825 169424 359386 198997 161380 638404 539555 206805 419206 345630 182699 319808 > 8¹¹² [i]