MinT - Best Known (70, 70+27, s)-Nets in Base 3

Best Known (70, 70+27, s)-Nets in Base 3

(70, 70+27, 204)-Net over F₃ — Constructive and digital

Digital (70, 97, 204)-net over F₃, using

3¹ times duplication [i] based on digital (69, 96, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 32, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(70, 70+27, 325)-Net over F₃ — Digital

Digital (70, 97, 325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+27, 9444)-Net in Base 3 — Upper bound on s

There is no (70, 97, 9445)-net in base 3, because

1 times m-reduction [i] would yield (70, 96, 9445)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6370 859760 333392 507582 163000 026627 953134 802107 > 3⁹⁶ [i]