MinT - Best Known (131−51, 131, s)-Nets in Base 3

Best Known (131−51, 131, s)-Nets in Base 3

(131−51, 131, 128)-Net over F₃ — Constructive and digital

Digital (80, 131, 128)-net over F₃, using

3 times m-reduction [i] based on digital (80, 134, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 67, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(131−51, 131, 141)-Net over F₃ — Digital

Digital (80, 131, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−51, 131, 1516)-Net in Base 3 — Upper bound on s

There is no (80, 131, 1517)-net in base 3, because

1 times m-reduction [i] would yield (80, 130, 1517)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 107 784292 068295 162975 650693 991220 332144 337144 558422 776890 311803 > 3¹³⁰ [i]