MinT - Best Known (82, 82+59, s)-Nets in Base 8

Best Known (82, 82+59, s)-Nets in Base 8

(82, 82+59, 354)-Net over F₈ — Constructive and digital

Digital (82, 141, 354)-net over F₈, using

9 times m-reduction [i] based on digital (82, 150, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 75, 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]

(82, 82+59, 493)-Net over F₈ — Digital

Digital (82, 141, 493)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+59, 38155)-Net in Base 8 — Upper bound on s

There is no (82, 141, 38156)-net in base 8, because

1 times m-reduction [i] would yield (82, 140, 38156)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 707777 672703 256341 705887 966040 198622 834101 376898 513281 013798 392694 653313 925996 851474 075652 238675 693892 259043 268856 763665 619520 > 8¹⁴⁰ [i]