MinT - Best Known (155, 155+68, s)-Nets in Base 3

Best Known (155, 155+68, s)-Nets in Base 3

(155, 155+68, 228)-Net over F₃ — Constructive and digital

Digital (155, 223, 228)-net over F₃, using

3¹ times duplication [i] based on digital (154, 222, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 74, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(155, 155+68, 463)-Net over F₃ — Digital

Digital (155, 223, 463)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+68, 9082)-Net in Base 3 — Upper bound on s

There is no (155, 223, 9083)-net in base 3, because

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]