MinT - Best Known (97−81, 97, s)-Nets in Base 16

Best Known (97−81, 97, s)-Nets in Base 16

(97−81, 97, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 97, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 97, 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]

(97−81, 97, 98)-Net over F₁₆ — Digital

Digital (16, 97, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 97, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(97−81, 97, 793)-Net in Base 16 — Upper bound on s

There is no (16, 97, 794)-net in base 16, because

1 times m-reduction [i] would yield (16, 96, 794)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 810664 916076 436211 972198 981501 441400 992703 213782 360802 316381 355333 237940 755730 704935 875878 870687 015939 847561 980776 > 16⁹⁶ [i]