MinT - Best Known (74−27, 74, s)-Nets in Base 3

Best Known (74−27, 74, s)-Nets in Base 3

(74−27, 74, 80)-Net over F₃ — Constructive and digital

Digital (47, 74, 80)-net over F₃, using

4 times m-reduction [i] based on digital (47, 78, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 39, 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]

(74−27, 74, 110)-Net over F₃ — Digital

Digital (47, 74, 110)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−27, 74, 1341)-Net in Base 3 — Upper bound on s

There is no (47, 74, 1342)-net in base 3, because

1 times m-reduction [i] would yield (47, 73, 1342)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 67926 015849 176333 887581 467288 747397 > 3⁷³ [i]