MinT - Best Known (171, 171+72, s)-Nets in Base 3

Best Known (171, 171+72, s)-Nets in Base 3

(171, 171+72, 264)-Net over F₃ — Constructive and digital

Digital (171, 243, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 81, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(171, 171+72, 547)-Net over F₃ — Digital

Digital (171, 243, 547)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+72, 11829)-Net in Base 3 — Upper bound on s

There is no (171, 243, 11830)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 253710 301331 001107 487016 690526 115049 207395 404881 979527 197042 978444 779164 060830 427934 222165 642642 410807 896120 359241 > 3²⁴³ [i]