MinT - Best Known (21, 115, s)-Nets in Base 16

Best Known (21, 115, s)-Nets in Base 16

(21, 115, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 115, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 115, 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]

(21, 115, 129)-Net over F₁₆ — Digital

Digital (21, 115, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 115, 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]

(21, 115, 1056)-Net in Base 16 — Upper bound on s

There is no (21, 115, 1057)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 095663 257597 118342 232812 257657 661781 584859 486868 794699 949518 391225 454154 132580 554629 171874 816875 218981 342957 253250 128675 954169 809676 276736 > 16¹¹⁵ [i]