MinT - Best Known (22, 22+97, s)-Nets in Base 16

Best Known (22, 22+97, s)-Nets in Base 16

(22, 22+97, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 119, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 119, 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]

(22, 22+97, 129)-Net over F₁₆ — Digital

Digital (22, 119, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 119, 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]

(22, 22+97, 1113)-Net in Base 16 — Upper bound on s

There is no (22, 119, 1114)-net in base 16, because

1 times m-reduction [i] would yield (22, 118, 1114)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12586 270345 325923 665252 527681 707609 114914 342196 164599 641266 018302 670601 859338 670498 988705 316897 708468 012739 890003 717805 791347 595602 323033 729206 > 16¹¹⁸ [i]