MinT - Best Known (54, 54+52, s)-Nets in Base 8

Best Known (54, 54+52, s)-Nets in Base 8

(54, 54+52, 160)-Net over F₈ — Constructive and digital

Digital (54, 106, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 53, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(54, 54+52, 198)-Net over F₈ — Digital

Digital (54, 106, 198)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+52, 7228)-Net in Base 8 — Upper bound on s

There is no (54, 106, 7229)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534865 603468 097980 631273 018944 781522 942259 457898 243421 256103 560858 162444 477244 265006 033992 208014 > 8¹⁰⁶ [i]