MinT - Best Known (232−53, 232, s)-Nets in Base 3

Best Known (232−53, 232, s)-Nets in Base 3

(232−53, 232, 640)-Net over F₃ — Constructive and digital

Digital (179, 232, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 58, 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]

(232−53, 232, 1386)-Net over F₃ — Digital

Digital (179, 232, 1386)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−53, 232, 91449)-Net in Base 3 — Upper bound on s

There is no (179, 232, 91450)-net in base 3, because

1 times m-reduction [i] would yield (179, 231, 91450)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 091122 346919 740169 316847 407914 172670 968136 623280 075118 732212 028957 698702 633333 980053 338333 818062 650623 435157 > 3²³¹ [i]