MinT - Best Known (235−61, 235, s)-Nets in Base 3

Best Known (235−61, 235, s)-Nets in Base 3

(235−61, 235, 288)-Net over F₃ — Constructive and digital

Digital (174, 235, 288)-net over F₃, using

t-expansion [i] based on digital (173, 235, 288)-net over F₃, using
- 8 times m-reduction [i] based on digital (173, 243, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 81, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(235−61, 235, 841)-Net over F₃ — Digital

Digital (174, 235, 841)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−61, 235, 31688)-Net in Base 3 — Upper bound on s

There is no (174, 235, 31689)-net in base 3, because

1 times m-reduction [i] would yield (174, 234, 31689)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4432 148616 415022 635679 818210 783194 790962 404072 024716 645265 713745 135363 510948 117666 617045 832142 971337 342654 190089 > 3²³⁴ [i]