MinT - Best Known (110−88, 110, s)-Nets in Base 16

Best Known (110−88, 110, s)-Nets in Base 16

(110−88, 110, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 110, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 110, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(110−88, 110, 129)-Net over F₁₆ — Digital

Digital (22, 110, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 110, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(110−88, 110, 1153)-Net in Base 16 — Upper bound on s

There is no (22, 110, 1154)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 876164 321316 339571 082719 632739 448565 989467 003516 555527 358700 686803 616989 156757 644580 196844 647354 293459 412643 840176 787785 768267 962016 > 16¹¹⁰ [i]