MinT - Best Known (72, 72+47, s)-Nets in Base 3

Best Known (72, 72+47, s)-Nets in Base 3

(72, 72+47, 80)-Net over F₃ — Constructive and digital

Digital (72, 119, 80)-net over F₃, using

9 times m-reduction [i] based on digital (72, 128, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 64, 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]

(72, 72+47, 125)-Net over F₃ — Digital

Digital (72, 119, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+47, 1299)-Net in Base 3 — Upper bound on s

There is no (72, 119, 1300)-net in base 3, because

1 times m-reduction [i] would yield (72, 118, 1300)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 200 492381 917521 813812 747715 829929 920418 431268 377928 415281 > 3¹¹⁸ [i]