MinT - Best Known (167, 167+70, s)-Nets in Base 3

Best Known (167, 167+70, s)-Nets in Base 3

(167, 167+70, 264)-Net over F₃ — Constructive and digital

Digital (167, 237, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 79, 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]

(167, 167+70, 540)-Net over F₃ — Digital

Digital (167, 237, 540)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+70, 11796)-Net in Base 3 — Upper bound on s

There is no (167, 237, 11797)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119717 207320 868917 604423 140308 511056 330294 052540 550131 172276 042436 682771 035622 234693 005468 425543 957110 826530 963755 > 3²³⁷ [i]