MinT - Best Known (131−39, 131, s)-Nets in Base 3

Best Known (131−39, 131, s)-Nets in Base 3

(131−39, 131, 192)-Net over F₃ — Constructive and digital

Digital (92, 131, 192)-net over F₃, using

1 times m-reduction [i] based on digital (92, 132, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 44, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(131−39, 131, 319)-Net over F₃ — Digital

Digital (92, 131, 319)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−39, 131, 7271)-Net in Base 3 — Upper bound on s

There is no (92, 131, 7272)-net in base 3, because

1 times m-reduction [i] would yield (92, 130, 7272)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106 375609 069264 986847 633278 120757 246764 456991 433891 679021 821217 > 3¹³⁰ [i]