MinT - Best Known (131−37, 131, s)-Nets in Base 3

Best Known (131−37, 131, s)-Nets in Base 3

(131−37, 131, 228)-Net over F₃ — Constructive and digital

Digital (94, 131, 228)-net over F₃, using

1 times m-reduction [i] based on digital (94, 132, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 44, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(131−37, 131, 384)-Net over F₃ — Digital

Digital (94, 131, 384)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−37, 131, 10525)-Net in Base 3 — Upper bound on s

There is no (94, 131, 10526)-net in base 3, because

1 times m-reduction [i] would yield (94, 130, 10526)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106 149104 999167 035274 575785 900811 047380 044266 570397 804375 865309 > 3¹³⁰ [i]