MinT - Best Known (127, 202, s)-Nets in Base 3

Best Known (127, 202, s)-Nets in Base 3

(127, 202, 156)-Net over F₃ — Constructive and digital

Digital (127, 202, 156)-net over F₃, using

8 times m-reduction [i] based on digital (127, 210, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 105, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(127, 202, 233)-Net over F₃ — Digital

Digital (127, 202, 233)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 202, 2826)-Net in Base 3 — Upper bound on s

There is no (127, 202, 2827)-net in base 3, because

1 times m-reduction [i] would yield (127, 201, 2827)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 800729 986761 140044 169761 605627 892292 999321 831767 006205 528609 014915 347527 129419 020886 646375 675151 > 3²⁰¹ [i]