MinT - Best Known (139−46, 139, s)-Nets in Base 9

Best Known (139−46, 139, s)-Nets in Base 9

(139−46, 139, 740)-Net over F₉ — Constructive and digital

Digital (93, 139, 740)-net over F₉, using

t-expansion [i] based on digital (91, 139, 740)-net over F₉, using
- 11 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 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]

(139−46, 139, 1975)-Net over F₉ — Digital

Digital (93, 139, 1975)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−46, 139, 689130)-Net in Base 9 — Upper bound on s

There is no (93, 139, 689131)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 362319 581569 611436 634500 979429 698629 315164 923203 430551 389008 136507 613222 860188 699750 071027 072372 642896 973460 134541 364943 968159 618921 > 9¹³⁹ [i]