MinT - Best Known (22, 22+81, s)-Nets in Base 16

Best Known (22, 22+81, s)-Nets in Base 16

(22, 22+81, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 103, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 103, 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+81, 129)-Net over F₁₆ — Digital

Digital (22, 103, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 103, 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+81, 1214)-Net in Base 16 — Upper bound on s

There is no (22, 103, 1215)-net in base 16, because

1 times m-reduction [i] would yield (22, 102, 1215)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 672 597135 554186 118417 321944 482559 115120 795505 559337 850208 895499 187351 629229 669334 734199 323806 489677 401771 190720 844673 757751 > 16¹⁰² [i]