MinT - Best Known (224−69, 224, s)-Nets in Base 3

Best Known (224−69, 224, s)-Nets in Base 3

(224−69, 224, 204)-Net over F₃ — Constructive and digital

Digital (155, 224, 204)-net over F₃, using

1 times m-reduction [i] based on digital (155, 225, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 75, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(224−69, 224, 450)-Net over F₃ — Digital

Digital (155, 224, 450)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−69, 224, 9082)-Net in Base 3 — Upper bound on s

There is no (155, 224, 9083)-net in base 3, because

1 times m-reduction [i] would yield (155, 223, 9083)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25056 981536 445070 359747 708879 863809 554792 042497 672122 513676 919562 916381 667433 756739 423231 919896 973840 537045 > 3²²³ [i]