MinT - Best Known (112−93, 112, s)-Nets in Base 16

Best Known (112−93, 112, s)-Nets in Base 16

(112−93, 112, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 112, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 112, 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]

(112−93, 112, 129)-Net over F₁₆ — Digital

Digital (19, 112, 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]

(112−93, 112, 940)-Net in Base 16 — Upper bound on s

There is no (19, 112, 941)-net in base 16, because

1 times m-reduction [i] would yield (19, 111, 941)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 518090 607812 059966 333168 333563 319805 985777 406046 163749 968475 145246 949043 366017 136833 477903 878662 096134 445482 076205 909279 545206 068416 > 16¹¹¹ [i]