MinT - Best Known (131−57, 131, s)-Nets in Base 3

Best Known (131−57, 131, s)-Nets in Base 3

(131−57, 131, 80)-Net over F₃ — Constructive and digital

Digital (74, 131, 80)-net over F₃, using

1 times m-reduction [i] based on digital (74, 132, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 66, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(131−57, 131, 103)-Net over F₃ — Digital

Digital (74, 131, 103)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−57, 131, 900)-Net in Base 3 — Upper bound on s

There is no (74, 131, 901)-net in base 3, because

1 times m-reduction [i] would yield (74, 130, 901)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 109 195243 200836 902845 927069 326830 673544 037170 632110 066308 410865 > 3¹³⁰ [i]