MinT - Best Known (26, 26+109, s)-Nets in Base 8

Best Known (26, 26+109, s)-Nets in Base 8

(26, 26+109, 65)-Net over F₈ — Constructive and digital

Digital (26, 135, 65)-net over F₈, using

t-expansion [i] based on digital (14, 135, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(26, 26+109, 86)-Net over F₈ — Digital

Digital (26, 135, 86)-net over F₈, using

t-expansion [i] based on digital (25, 135, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(26, 26+109, 488)-Net in Base 8 — Upper bound on s

There is no (26, 135, 489)-net in base 8, because

1 times m-reduction [i] would yield (26, 134, 489)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 246162 378843 619849 430521 847034 316318 126423 216249 725414 882246 666640 170070 646760 605360 130325 792794 306366 657806 960967 547568 > 8¹³⁴ [i]