MinT - Best Known (225−95, 225, s)-Nets in Base 3

Best Known (225−95, 225, s)-Nets in Base 3

(225−95, 225, 148)-Net over F₃ — Constructive and digital

Digital (130, 225, 148)-net over F₃, using

1 times m-reduction [i] based on digital (130, 226, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 113, 74)-net over F₉, using
  - net from sequence [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]

(225−95, 225, 178)-Net over F₃ — Digital

Digital (130, 225, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−95, 225, 1679)-Net in Base 3 — Upper bound on s

There is no (130, 225, 1680)-net in base 3, because

1 times m-reduction [i] would yield (130, 224, 1680)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75245 595091 625178 076589 406726 916423 853281 379891 450343 209523 091492 753224 496895 960591 772044 695515 577616 198337 > 3²²⁴ [i]