MinT - Best Known (14, 81, s)-Nets in Base 16

Best Known (14, 81, s)-Nets in Base 16

(14, 81, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 81, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 81, 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]

(14, 81, 97)-Net over F₁₆ — Digital

Digital (14, 81, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 81, 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]

(14, 81, 710)-Net in Base 16 — Upper bound on s

There is no (14, 81, 711)-net in base 16, because

1 times m-reduction [i] would yield (14, 80, 711)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 208244 610137 763425 239493 894028 299415 243754 475067 536124 100381 666976 585886 839900 638613 398374 542996 > 16⁸⁰ [i]