MinT - Best Known (248−59, 248, s)-Nets in Base 3

Best Known (248−59, 248, s)-Nets in Base 3

(248−59, 248, 464)-Net over F₃ — Constructive and digital

Digital (189, 248, 464)-net over F₃, using

t-expansion [i] based on digital (188, 248, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 62, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(248−59, 248, 1239)-Net over F₃ — Digital

Digital (189, 248, 1239)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−59, 248, 67556)-Net in Base 3 — Upper bound on s

There is no (189, 248, 67557)-net in base 3, because

1 times m-reduction [i] would yield (189, 247, 67557)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7064 517725 682599 565816 249851 076361 352741 267151 485135 936873 973152 014802 708328 310714 153340 047837 032698 877913 851517 291899 > 3²⁴⁷ [i]