MinT - Best Known (83, 130, s)-Nets in Base 9

Best Known (83, 130, s)-Nets in Base 9

(83, 130, 740)-Net over F₉ — Constructive and digital

Digital (83, 130, 740)-net over F₉, using

4 times m-reduction [i] based on digital (83, 134, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 67, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(83, 130, 1142)-Net over F₉ — Digital

Digital (83, 130, 1142)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 130, 265093)-Net in Base 9 — Upper bound on s

There is no (83, 130, 265094)-net in base 9, because

1 times m-reduction [i] would yield (83, 129, 265094)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1251 110652 397559 463287 297965 363522 613368 864608 382624 026714 380674 315798 967469 834415 839189 735230 038973 965740 700754 172962 429073 > 9¹²⁹ [i]