MinT - Best Known (52, 52+70, s)-Nets in Base 16

Best Known (52, 52+70, s)-Nets in Base 16

(52, 52+70, 243)-Net over F₁₆ — Constructive and digital

Digital (52, 122, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 122, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(52, 52+70, 255)-Net over F₁₆ — Digital

Digital (52, 122, 255)-net over F₁₆, using

t-expansion [i] based on digital (50, 122, 255)-net over F₁₆, using
- net from sequence [i] based on digital (50, 254)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 50 and N(F) ≥ 255, using
    - a curve from the manYPoints database [i]

(52, 52+70, 14581)-Net in Base 16 — Upper bound on s

There is no (52, 122, 14582)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 799 268713 603257 172054 717858 057048 870925 248500 749739 866262 238328 006477 434798 359374 859724 869554 752507 141735 205968 633605 162422 972059 731980 882740 745926 > 16¹²² [i]