MinT - Best Known (225−113, 225, s)-Nets in Base 3

Best Known (225−113, 225, s)-Nets in Base 3

(225−113, 225, 74)-Net over F₃ — Constructive and digital

Digital (112, 225, 74)-net over F₃, using

t-expansion [i] based on digital (107, 225, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [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]

(225−113, 225, 110)-Net over F₃ — Digital

Digital (112, 225, 110)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−113, 225, 825)-Net in Base 3 — Upper bound on s

There is no (112, 225, 826)-net in base 3, because

1 times m-reduction [i] would yield (112, 224, 826)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79308 721326 635338 729469 688469 250677 934703 378310 880411 450541 995980 467932 562597 259613 453748 379465 256073 663153 > 3²²⁴ [i]