MinT - Best Known (92−71, 92, s)-Nets in Base 16

Best Known (92−71, 92, s)-Nets in Base 16

(92−71, 92, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 92, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 92, 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]

(92−71, 92, 129)-Net over F₁₆ — Digital

Digital (21, 92, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 92, 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]

(92−71, 92, 1233)-Net in Base 16 — Upper bound on s

There is no (21, 92, 1234)-net in base 16, because

1 times m-reduction [i] would yield (21, 91, 1234)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 38 053366 815827 419275 688751 740377 990104 239261 300819 659087 487676 443460 130230 239026 276823 797894 819858 415631 340976 > 16⁹¹ [i]