MinT - Best Known (73−25, 73, s)-Nets in Base 3

Best Known (73−25, 73, s)-Nets in Base 3

(73−25, 73, 80)-Net over F₃ — Constructive and digital

Digital (48, 73, 80)-net over F₃, using

7 times m-reduction [i] based on digital (48, 80, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 40, 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]

(73−25, 73, 131)-Net over F₃ — Digital

Digital (48, 73, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−25, 73, 1916)-Net in Base 3 — Upper bound on s

There is no (48, 73, 1917)-net in base 3, because

1 times m-reduction [i] would yield (48, 72, 1917)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22624 616491 552069 902942 545751 519217 > 3⁷² [i]