MinT - Best Known (89, 89+75, s)-Nets in Base 8

Best Known (89, 89+75, s)-Nets in Base 8

(89, 89+75, 354)-Net over F₈ — Constructive and digital

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+75, 383)-Net over F₈ — Digital

Digital (89, 164, 383)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+75, 19896)-Net in Base 8 — Upper bound on s

There is no (89, 164, 19897)-net in base 8, because

1 times m-reduction [i] would yield (89, 163, 19897)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1598 894234 488896 106968 830532 436531 133381 441113 315256 243331 897902 746383 622170 343788 217349 219463 208581 255410 027925 746384 887622 103627 918651 657617 465208 > 8¹⁶³ [i]