MinT - Best Known (112, 112+111, s)-Nets in Base 3

Best Known (112, 112+111, s)-Nets in Base 3

(112, 112+111, 74)-Net over F₃ — Constructive and digital

Digital (112, 223, 74)-net over F₃, using

t-expansion [i] based on digital (107, 223, 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]

(112, 112+111, 111)-Net over F₃ — Digital

Digital (112, 223, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+111, 846)-Net in Base 3 — Upper bound on s

There is no (112, 223, 847)-net in base 3, because

1 times m-reduction [i] would yield (112, 222, 847)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8725 312108 408844 663961 572358 191068 020507 927032 644702 513575 687668 050322 622426 224170 324188 265583 927245 972947 > 3²²² [i]