MinT - Best Known (88−45, 88, s)-Nets in Base 16

Best Known (88−45, 88, s)-Nets in Base 16

(88−45, 88, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 88, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 88, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(88−45, 88, 289)-Net over F₁₆ — Digital

Digital (43, 88, 289)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−45, 88, 34862)-Net in Base 16 — Upper bound on s

There is no (43, 88, 34863)-net in base 16, because

1 times m-reduction [i] would yield (43, 87, 34863)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 573 514557 102247 043484 571544 706571 449907 552654 679097 446691 861916 353020 625311 807929 473434 291879 087564 100766 > 16⁸⁷ [i]