MinT - Best Known (163−63, 163, s)-Nets in Base 3

Best Known (163−63, 163, s)-Nets in Base 3

(163−63, 163, 148)-Net over F₃ — Constructive and digital

Digital (100, 163, 148)-net over F₃, using

3 times m-reduction [i] based on digital (100, 166, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 83, 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]

(163−63, 163, 173)-Net over F₃ — Digital

Digital (100, 163, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−63, 163, 1903)-Net in Base 3 — Upper bound on s

There is no (100, 163, 1904)-net in base 3, because

1 times m-reduction [i] would yield (100, 162, 1904)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199137 218558 078085 360232 787945 199703 550169 044333 047641 429546 770694 274606 598465 > 3¹⁶² [i]