MinT - Best Known (224−51, 224, s)-Nets in Base 3

Best Known (224−51, 224, s)-Nets in Base 3

(224−51, 224, 640)-Net over F₃ — Constructive and digital

Digital (173, 224, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 56, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(224−51, 224, 1362)-Net over F₃ — Digital

Digital (173, 224, 1362)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−51, 224, 91706)-Net in Base 3 — Upper bound on s

There is no (173, 224, 91707)-net in base 3, because

1 times m-reduction [i] would yield (173, 223, 91707)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25007 269153 478356 069485 484746 635191 118257 111258 500598 946216 826312 999477 308044 686058 403679 635642 882489 543559 > 3²²³ [i]