MinT - Best Known (131, 181, s)-Nets in Base 3

Best Known (131, 181, s)-Nets in Base 3

(131, 181, 282)-Net over F₃ — Constructive and digital

Digital (131, 181, 282)-net over F₃, using

3¹ times duplication [i] based on digital (130, 180, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 60, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(131, 181, 538)-Net over F₃ — Digital

Digital (131, 181, 538)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 181, 14461)-Net in Base 3 — Upper bound on s

There is no (131, 181, 14462)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 653581 307580 516109 756852 578257 620317 707150 804259 155522 736438 662861 080849 162449 663309 > 3¹⁸¹ [i]