MinT - Best Known (69, 69+25, s)-Nets in Base 3

Best Known (69, 69+25, s)-Nets in Base 3

(69, 69+25, 228)-Net over F₃ — Constructive and digital

Digital (69, 94, 228)-net over F₃, using

3¹ times duplication [i] based on digital (68, 93, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 31, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(69, 69+25, 374)-Net over F₃ — Digital

Digital (69, 94, 374)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+25, 13171)-Net in Base 3 — Upper bound on s

There is no (69, 94, 13172)-net in base 3, because

1 times m-reduction [i] would yield (69, 93, 13172)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 235 716510 928000 606368 372306 958840 486130 677121 > 3⁹³ [i]