MinT - Best Known (92, 92+107, s)-Nets in Base 3

Best Known (92, 92+107, s)-Nets in Base 3

(92, 92+107, 64)-Net over F₃ — Constructive and digital

Digital (92, 199, 64)-net over F₃, using

t-expansion [i] based on digital (89, 199, 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+107, 96)-Net over F₃ — Digital

Digital (92, 199, 96)-net over F₃, using

t-expansion [i] based on digital (89, 199, 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+107, 573)-Net in Base 3 — Upper bound on s

There is no (92, 199, 574)-net in base 3, because

1 times m-reduction [i] would yield (92, 198, 574)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 31317 613301 030336 297745 231997 493988 972267 301891 030520 344292 429283 200678 998795 962724 708749 421365 > 3¹⁹⁸ [i]