MinT - Best Known (89, 89+71, s)-Nets in Base 8

Best Known (89, 89+71, s)-Nets in Base 8

(89, 89+71, 354)-Net over F₈ — Constructive and digital

Digital (89, 160, 354)-net over F₈, using

4 times m-reduction [i] based on digital (89, 164, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 82, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(89, 89+71, 424)-Net over F₈ — Digital

Digital (89, 160, 424)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+71, 25141)-Net in Base 8 — Upper bound on s

There is no (89, 160, 25142)-net in base 8, because

1 times m-reduction [i] would yield (89, 159, 25142)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390376 688151 718582 631487 925508 322576 826356 481296 765014 051935 617709 372028 498354 591830 125224 022264 439712 870054 416591 356384 904094 400856 682060 296866 > 8¹⁵⁹ [i]