MinT - Best Known (130−86, 130, s)-Nets in Base 16

Best Known (130−86, 130, s)-Nets in Base 16

(130−86, 130, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 130, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 130, 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]

(130−86, 130, 226)-Net over F₁₆ — Digital

Digital (44, 130, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 130, 226)-net over F₁₆, using
- net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
    - Drinfeld modules of rank 1 [i]

(130−86, 130, 4893)-Net in Base 16 — Upper bound on s

There is no (44, 130, 4894)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 444045 132509 044233 917486 150247 064847 362377 693397 677636 769595 720919 372247 637890 395309 360632 046252 298998 921991 419395 693843 773084 400279 261111 937248 030293 914256 > 16¹³⁰ [i]