MinT - Best Known (39−25, 39, s)-Nets in Base 16

Best Known (39−25, 39, s)-Nets in Base 16

(39−25, 39, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 39, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 39, 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]

(39−25, 39, 80)-Net in Base 16 — Constructive

(14, 39, 80)-net in base 16, using

base change [i] based on digital (1, 26, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(39−25, 39, 97)-Net over F₁₆ — Digital

Digital (14, 39, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 39, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(39−25, 39, 2286)-Net in Base 16 — Upper bound on s

There is no (14, 39, 2287)-net in base 16, because

1 times m-reduction [i] would yield (14, 38, 2287)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 5731 628714 108983 038964 618737 661131 672672 583711 > 16³⁸ [i]