MinT - Best Known (72, 72+53, s)-Nets in Base 3

Best Known (72, 72+53, s)-Nets in Base 3

(72, 72+53, 80)-Net over F₃ — Constructive and digital

Digital (72, 125, 80)-net over F₃, using

3 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+53, 107)-Net over F₃ — Digital

Digital (72, 125, 107)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+53, 969)-Net in Base 3 — Upper bound on s

There is no (72, 125, 970)-net in base 3, because

1 times m-reduction [i] would yield (72, 124, 970)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 146952 960688 340846 314577 652921 612229 127793 764493 225936 444789 > 3¹²⁴ [i]