MinT - Best Known (175, 175+57, s)-Nets in Base 3

Best Known (175, 175+57, s)-Nets in Base 3

(175, 175+57, 400)-Net over F₃ — Constructive and digital

Digital (175, 232, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 58, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(175, 175+57, 1029)-Net over F₃ — Digital

Digital (175, 232, 1029)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+57, 48750)-Net in Base 3 — Upper bound on s

There is no (175, 232, 48751)-net in base 3, because

1 times m-reduction [i] would yield (175, 231, 48751)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 094411 799461 657924 026312 623441 562603 378721 027279 168150 526839 745871 784199 775010 528313 283400 181305 791236 354761 > 3²³¹ [i]