MinT - Best Known (83, 83+35, s)-Nets in Base 9

Best Known (83, 83+35, s)-Nets in Base 9

(83, 83+35, 740)-Net over F₉ — Constructive and digital

Digital (83, 118, 740)-net over F₉, using

16 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, 83+35, 3486)-Net over F₉ — Digital

Digital (83, 118, 3486)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+35, 3313505)-Net in Base 9 — Upper bound on s

There is no (83, 118, 3313506)-net in base 9, because

1 times m-reduction [i] would yield (83, 117, 3313506)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4429 714806 638959 481283 300335 449471 675533 766350 383574 256872 418569 249771 759697 305429 249418 400049 831952 639465 386513 > 9¹¹⁷ [i]