MinT - Best Known (91, 131, s)-Nets in Base 9

Best Known (91, 131, s)-Nets in Base 9

(91, 131, 740)-Net over F₉ — Constructive and digital

Digital (91, 131, 740)-net over F₉, using

19 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]

(91, 131, 3107)-Net over F₉ — Digital

Digital (91, 131, 3107)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 131, 1847148)-Net in Base 9 — Upper bound on s

There is no (91, 131, 1847149)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101337 487766 495659 589765 923972 359821 358216 476670 183693 430161 814367 384327 992877 389834 344223 080539 395223 398079 319207 667409 344161 > 9¹³¹ [i]