MinT - Best Known (21, 21+78, s)-Nets in Base 16

Best Known (21, 21+78, s)-Nets in Base 16

(21, 21+78, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 99, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 99, 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, 21+78, 129)-Net over F₁₆ — Digital

Digital (21, 99, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 99, 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, 21+78, 1147)-Net in Base 16 — Upper bound on s

There is no (21, 99, 1148)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 162181 740107 186821 216925 729703 974356 883490 576011 605365 564950 283783 856105 282264 234719 486934 070331 887045 510035 018773 553306 > 16⁹⁹ [i]