MinT - Best Known (117−34, 117, s)-Nets in Base 9

Best Known (117−34, 117, s)-Nets in Base 9

(117−34, 117, 750)-Net over F₉ — Constructive and digital

Digital (83, 117, 750)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 17, 10)-net over F₉, using
  - net from sequence [i] based on digital (0, 9)-sequence over F₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 0 and N(F) ≥ 10, using
      - the rational function field F₉(x) [i]
    - Niederreiter sequence [i]
2. digital (66, 100, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 50, 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]

(117−34, 117, 3993)-Net over F₉ — Digital

Digital (83, 117, 3993)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−34, 117, 3313505)-Net in Base 9 — Upper bound on s

There is no (83, 117, 3313506)-net in base 9, because

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]