MinT - Best Known (97, 97+135, s)-Nets in Base 3

Best Known (97, 97+135, s)-Nets in Base 3

(97, 97+135, 64)-Net over F₃ — Constructive and digital

Digital (97, 232, 64)-net over F₃, using

t-expansion [i] based on digital (89, 232, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(97, 97+135, 96)-Net over F₃ — Digital

Digital (97, 232, 96)-net over F₃, using

t-expansion [i] based on digital (89, 232, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(97, 97+135, 505)-Net in Base 3 — Upper bound on s

There is no (97, 232, 506)-net in base 3, because

1 times m-reduction [i] would yield (97, 231, 506)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 167 115885 528611 524542 451858 128037 402106 787722 660791 616286 132313 265877 747157 254704 952275 185965 987912 961218 235761 > 3²³¹ [i]