MinT - Best Known (16, 91, s)-Nets in Base 16

Best Known (16, 91, s)-Nets in Base 16

(16, 91, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 91, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 91, 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]

(16, 91, 98)-Net over F₁₆ — Digital

Digital (16, 91, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 91, 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]

(16, 91, 809)-Net in Base 16 — Upper bound on s

There is no (16, 91, 810)-net in base 16, because

1 times m-reduction [i] would yield (16, 90, 810)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 449889 275455 321329 960845 391171 769816 503608 023620 015296 993951 943592 806511 477567 879830 179010 779740 290545 834426 > 16⁹⁰ [i]