MinT - Best Known (52, 102, s)-Nets in Base 8

Best Known (52, 102, s)-Nets in Base 8

(52, 102, 160)-Net over F₈ — Constructive and digital

Digital (52, 102, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 51, 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]

(52, 102, 193)-Net over F₈ — Digital

Digital (52, 102, 193)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 102, 7017)-Net in Base 8 — Upper bound on s

There is no (52, 102, 7018)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 673173 039993 626762 633336 433319 208837 631753 306600 246771 264198 970486 253313 919063 032083 477818 > 8¹⁰² [i]