MinT - Best Known (71−25, 71, s)-Nets in Base 3

Best Known (71−25, 71, s)-Nets in Base 3

(71−25, 71, 80)-Net over F₃ — Constructive and digital

Digital (46, 71, 80)-net over F₃, using

5 times m-reduction [i] based on digital (46, 76, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 38, 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]

(71−25, 71, 118)-Net over F₃ — Digital

Digital (46, 71, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−25, 71, 1593)-Net in Base 3 — Upper bound on s

There is no (46, 71, 1594)-net in base 3, because

1 times m-reduction [i] would yield (46, 70, 1594)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2507 465606 387857 437485 695625 973369 > 3⁷⁰ [i]