MinT - Best Known (82−25, 82, s)-Nets in Base 3

Best Known (82−25, 82, s)-Nets in Base 3

(82−25, 82, 144)-Net over F₃ — Constructive and digital

Digital (57, 82, 144)-net over F₃, using

3¹ times duplication [i] based on digital (56, 81, 144)-net over F₃, using
- trace code for nets [i] based on digital (2, 27, 48)-net over F₂₇, using
  - net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]

(82−25, 82, 208)-Net over F₃ — Digital

Digital (57, 82, 208)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−25, 82, 4382)-Net in Base 3 — Upper bound on s

There is no (57, 82, 4383)-net in base 3, because

1 times m-reduction [i] would yield (57, 81, 4383)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 443 528634 565347 300909 118839 459791 598057 > 3⁸¹ [i]