MinT - Best Known (131, 131+89, s)-Nets in Base 3

Best Known (131, 131+89, s)-Nets in Base 3

(131, 131+89, 148)-Net over F₃ — Constructive and digital

Digital (131, 220, 148)-net over F₃, using

8 times m-reduction [i] based on digital (131, 228, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 114, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(131, 131+89, 197)-Net over F₃ — Digital

Digital (131, 220, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+89, 2001)-Net in Base 3 — Upper bound on s

There is no (131, 220, 2002)-net in base 3, because

1 times m-reduction [i] would yield (131, 219, 2002)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 310 693126 704103 047404 811747 026511 195425 339072 486622 905255 074052 926864 668512 731484 138773 024986 929391 354297 > 3²¹⁹ [i]