MinT - Best Known (85−25, 85, s)-Nets in Base 3

Best Known (85−25, 85, s)-Nets in Base 3

(85−25, 85, 156)-Net over F₃ — Constructive and digital

Digital (60, 85, 156)-net over F₃, using

3¹ times duplication [i] based on digital (59, 84, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 28, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(85−25, 85, 243)-Net over F₃ — Digital

Digital (60, 85, 243)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−25, 85, 5771)-Net in Base 3 — Upper bound on s

There is no (60, 85, 5772)-net in base 3, because

1 times m-reduction [i] would yield (60, 84, 5772)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11975 764055 321215 207450 799027 802305 608641 > 3⁸⁴ [i]