MinT - Best Known (110−66, 110, s)-Nets in Base 16

Best Known (110−66, 110, s)-Nets in Base 16

(110−66, 110, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 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]

(110−66, 110, 226)-Net over F₁₆ — Digital

Digital (44, 110, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 110, 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]

(110−66, 110, 9039)-Net in Base 16 — Upper bound on s

There is no (44, 110, 9040)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 849011 964509 347464 005535 654002 176120 527753 015997 164754 386081 531663 721112 864674 092200 201407 035090 382836 665955 431606 966484 201830 613926 > 16¹¹⁰ [i]