MinT - Best Known (92, 237, s)-Nets in Base 3

Best Known (92, 237, s)-Nets in Base 3

(92, 237, 64)-Net over F₃ — Constructive and digital

Digital (92, 237, 64)-net over F₃, using

t-expansion [i] based on digital (89, 237, 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, 237, 96)-Net over F₃ — Digital

Digital (92, 237, 96)-net over F₃, using

t-expansion [i] based on digital (89, 237, 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, 237, 438)-Net in Base 3 — Upper bound on s

There is no (92, 237, 439)-net in base 3, because

1 times m-reduction [i] would yield (92, 236, 439)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41957 080127 143659 150862 824839 776482 552094 288925 397516 522011 084175 472013 290862 120457 113255 853697 348335 660736 605681 > 3²³⁶ [i]