MinT - Best Known (20, 20+85, s)-Nets in Base 16

Best Known (20, 20+85, s)-Nets in Base 16

(20, 20+85, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 105, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 105, 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]

(20, 20+85, 129)-Net over F₁₆ — Digital

Digital (20, 105, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 105, 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]

(20, 20+85, 1032)-Net in Base 16 — Upper bound on s

There is no (20, 105, 1033)-net in base 16, because

1 times m-reduction [i] would yield (20, 104, 1033)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 175805 422843 517281 359872 065174 100904 020986 307448 717418 379294 408671 858530 283220 286055 780440 262600 581735 239745 184973 341104 918016 > 16¹⁰⁴ [i]