MinT - Best Known (112−33, 112, s)-Nets in Base 9

Best Known (112−33, 112, s)-Nets in Base 9

(112−33, 112, 740)-Net over F₉ — Constructive and digital

Digital (79, 112, 740)-net over F₉, using

14 times m-reduction [i] based on digital (79, 126, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 63, 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]

(112−33, 112, 3512)-Net over F₉ — Digital

Digital (79, 112, 3512)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−33, 112, 3544091)-Net in Base 9 — Upper bound on s

There is no (79, 112, 3544092)-net in base 9, because

1 times m-reduction [i] would yield (79, 111, 3544092)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8335 249755 462678 412538 584708 699383 741369 293952 629248 538659 436062 091360 833716 242795 407787 585634 468713 456129 > 9¹¹¹ [i]