MinT - Best Known (92, 92+117, s)-Nets in Base 3

Best Known (92, 92+117, s)-Nets in Base 3

(92, 92+117, 64)-Net over F₃ — Constructive and digital

Digital (92, 209, 64)-net over F₃, using

t-expansion [i] based on digital (89, 209, 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]

(92, 92+117, 96)-Net over F₃ — Digital

Digital (92, 209, 96)-net over F₃, using

t-expansion [i] based on digital (89, 209, 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]

(92, 92+117, 521)-Net in Base 3 — Upper bound on s

There is no (92, 209, 522)-net in base 3, because

1 times m-reduction [i] would yield (92, 208, 522)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1766 316957 356358 112952 396376 615501 342549 476325 039178 214740 472631 713084 490651 888674 535577 336195 196469 > 3²⁰⁸ [i]