MinT - Best Known (97, 97+59, s)-Nets in Base 3

Best Known (97, 97+59, s)-Nets in Base 3

(97, 97+59, 148)-Net over F₃ — Constructive and digital

Digital (97, 156, 148)-net over F₃, using

4 times m-reduction [i] based on digital (97, 160, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 80, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(97, 97+59, 177)-Net over F₃ — Digital

Digital (97, 156, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+59, 2042)-Net in Base 3 — Upper bound on s

There is no (97, 156, 2043)-net in base 3, because

1 times m-reduction [i] would yield (97, 155, 2043)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 90 075224 071140 039430 664665 438667 188411 152489 688890 311927 668209 100499 262015 > 3¹⁵⁵ [i]