MinT - Best Known (132−41, 132, s)-Nets in Base 3

Best Known (132−41, 132, s)-Nets in Base 3

(132−41, 132, 156)-Net over F₃ — Constructive and digital

Digital (91, 132, 156)-net over F₃, using

6 times m-reduction [i] based on digital (91, 138, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 69, 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]

(132−41, 132, 280)-Net over F₃ — Digital

Digital (91, 132, 280)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−41, 132, 5519)-Net in Base 3 — Upper bound on s

There is no (91, 132, 5520)-net in base 3, because

1 times m-reduction [i] would yield (91, 131, 5520)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 319 037457 703709 199498 679901 369803 898419 083242 239743 967805 677953 > 3¹³¹ [i]