MinT - Best Known (131−35, 131, s)-Nets in Base 3

Best Known (131−35, 131, s)-Nets in Base 3

(131−35, 131, 252)-Net over F₃ — Constructive and digital

Digital (96, 131, 252)-net over F₃, using

1 times m-reduction [i] based on digital (96, 132, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 44, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(131−35, 131, 471)-Net over F₃ — Digital

Digital (96, 131, 471)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−35, 131, 15960)-Net in Base 3 — Upper bound on s

There is no (96, 131, 15961)-net in base 3, because

1 times m-reduction [i] would yield (96, 130, 15961)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106 191110 310637 486791 168611 377552 612826 816117 910484 469325 780339 > 3¹³⁰ [i]