MinT - Best Known (225−59, 225, s)-Nets in Base 3

Best Known (225−59, 225, s)-Nets in Base 3

(225−59, 225, 288)-Net over F₃ — Constructive and digital

Digital (166, 225, 288)-net over F₃, using

t-expansion [i] based on digital (165, 225, 288)-net over F₃, using
- 6 times m-reduction [i] based on digital (165, 231, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 77, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(225−59, 225, 780)-Net over F₃ — Digital

Digital (166, 225, 780)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−59, 225, 28249)-Net in Base 3 — Upper bound on s

There is no (166, 225, 28250)-net in base 3, because

1 times m-reduction [i] would yield (166, 224, 28250)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75086 249774 342731 559527 124985 456787 029075 855945 568906 295692 395369 667016 992635 418645 248076 708219 698127 397661 > 3²²⁴ [i]