MinT - Best Known (127−36, 127, s)-Nets in Base 9

Best Known (127−36, 127, s)-Nets in Base 9

(127−36, 127, 772)-Net over F₉ — Constructive and digital

Digital (91, 127, 772)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 23, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (68, 104, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 52, 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]

(127−36, 127, 5061)-Net over F₉ — Digital

Digital (91, 127, 5061)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−36, 127, 5102114)-Net in Base 9 — Upper bound on s

There is no (91, 127, 5102115)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 445415 459342 172738 813394 580468 395390 627733 443445 750487 875865 712855 931880 305785 482542 119182 685737 716925 606466 678494 991665 > 9¹²⁷ [i]