MinT - Best Known (126−36, 126, s)-Nets in Base 9

Best Known (126−36, 126, s)-Nets in Base 9

(126−36, 126, 770)-Net over F₉ — Constructive and digital

Digital (90, 126, 770)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (4, 22, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [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]

(126−36, 126, 4754)-Net over F₉ — Digital

Digital (90, 126, 4754)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−36, 126, 4515819)-Net in Base 9 — Upper bound on s

There is no (90, 126, 4515820)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716155 209426 405532 942322 476185 269557 071432 846405 895079 391253 085893 458353 580891 452954 718596 671192 231413 907253 319936 940097 > 9¹²⁶ [i]