MinT - Best Known (241−74, 241, s)-Nets in Base 3

Best Known (241−74, 241, s)-Nets in Base 3

(241−74, 241, 228)-Net over F₃ — Constructive and digital

Digital (167, 241, 228)-net over F₃, using

3¹ times duplication [i] based on digital (166, 240, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 80, 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]

(241−74, 241, 485)-Net over F₃ — Digital

Digital (167, 241, 485)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−74, 241, 9352)-Net in Base 3 — Upper bound on s

There is no (167, 241, 9353)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 706060 927161 855823 441444 298195 617623 113283 761908 422348 640933 915685 875877 419639 838299 521668 846107 585677 156325 341443 > 3²⁴¹ [i]