MinT - Best Known (104−58, 104, s)-Nets in Base 16

Best Known (104−58, 104, s)-Nets in Base 16

(104−58, 104, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 104, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 104, 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]

(104−58, 104, 243)-Net over F₁₆ — Digital

Digital (46, 104, 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]

(104−58, 104, 16174)-Net in Base 16 — Upper bound on s

There is no (46, 104, 16175)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 169429 596719 409209 044882 515320 700196 755484 734703 844441 235526 055507 142525 173950 359490 583466 922010 781633 274708 038015 006779 569876 > 16¹⁰⁴ [i]