MinT - Best Known (46, 46+46, s)-Nets in Base 8

Best Known (46, 46+46, s)-Nets in Base 8

(46, 46+46, 130)-Net over F₈ — Constructive and digital

Digital (46, 92, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 46, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(46, 46+46, 163)-Net over F₈ — Digital

Digital (46, 92, 163)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+46, 5502)-Net in Base 8 — Upper bound on s

There is no (46, 92, 5503)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 121457 868843 347235 620853 185978 531331 573469 621922 158373 230923 998670 244961 863188 470496 > 8⁹² [i]