MinT - Best Known (83−27, 83, s)-Nets in Base 3

Best Known (83−27, 83, s)-Nets in Base 3

(83−27, 83, 128)-Net over F₃ — Constructive and digital

Digital (56, 83, 128)-net over F₃, using

3 times m-reduction [i] based on digital (56, 86, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 43, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(83−27, 83, 169)-Net over F₃ — Digital

Digital (56, 83, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−27, 83, 2884)-Net in Base 3 — Upper bound on s

There is no (56, 83, 2885)-net in base 3, because

1 times m-reduction [i] would yield (56, 82, 2885)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1334 659427 842111 721062 722421 963553 544571 > 3⁸² [i]