MinT - Best Known (131−43, 131, s)-Nets in Base 3

Best Known (131−43, 131, s)-Nets in Base 3

(131−43, 131, 156)-Net over F₃ — Constructive and digital

Digital (88, 131, 156)-net over F₃, using

1 times m-reduction [i] based on digital (88, 132, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 66, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(131−43, 131, 234)-Net over F₃ — Digital

Digital (88, 131, 234)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−43, 131, 3879)-Net in Base 3 — Upper bound on s

There is no (88, 131, 3880)-net in base 3, because

1 times m-reduction [i] would yield (88, 130, 3880)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106 342489 216899 581079 762802 144450 566623 166946 166411 886487 271121 > 3¹³⁰ [i]