MinT - Best Known (110−63, 110, s)-Nets in Base 16

Best Known (110−63, 110, s)-Nets in Base 16

(110−63, 110, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 110, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 110, 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]

(110−63, 110, 243)-Net over F₁₆ — Digital

Digital (47, 110, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 110, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(110−63, 110, 14166)-Net in Base 16 — Upper bound on s

There is no (47, 110, 14167)-net in base 16, because

1 times m-reduction [i] would yield (47, 109, 14167)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177674 889037 352496 457079 367473 508302 851797 590745 232871 492936 470828 315655 526682 967183 803815 145040 942436 241547 111395 582763 608089 374656 > 16¹⁰⁹ [i]