MinT - Best Known (83, 144, s)-Nets in Base 3

Best Known (83, 144, s)-Nets in Base 3

(83, 144, 80)-Net over F₃ — Constructive and digital

Digital (83, 144, 80)-net over F₃, using

6 times m-reduction [i] based on digital (83, 150, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 75, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(83, 144, 120)-Net over F₃ — Digital

Digital (83, 144, 120)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 144, 1103)-Net in Base 3 — Upper bound on s

There is no (83, 144, 1104)-net in base 3, because

1 times m-reduction [i] would yield (83, 143, 1104)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 172 285591 160056 397446 031415 072859 119398 204727 670149 578983 420982 822113 > 3¹⁴³ [i]