MinT - Best Known (86−42, 86, s)-Nets in Base 8

Best Known (86−42, 86, s)-Nets in Base 8

(86−42, 86, 160)-Net over F₈ — Constructive and digital

Digital (44, 86, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 43, 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]

(86−42, 86, 170)-Net over F₈ — Digital

Digital (44, 86, 170)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−42, 86, 6178)-Net in Base 8 — Upper bound on s

There is no (44, 86, 6179)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 464678 227394 766510 529342 426780 598705 028565 251279 799231 690900 293163 066799 826864 > 8⁸⁶ [i]