MinT - Best Known (87−43, 87, s)-Nets in Base 8

Best Known (87−43, 87, s)-Nets in Base 8

(87−43, 87, 130)-Net over F₈ — Constructive and digital

Digital (44, 87, 130)-net over F₈, using

1 times m-reduction [i] based on digital (44, 88, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 44, 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]

(87−43, 87, 164)-Net over F₈ — Digital

Digital (44, 87, 164)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−43, 87, 6178)-Net in Base 8 — Upper bound on s

There is no (44, 87, 6179)-net in base 8, because

1 times m-reduction [i] would yield (44, 86, 6179)-net in base 8, but
- 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]