MinT - Best Known (125−101, 125, s)-Nets in Base 16

Best Known (125−101, 125, s)-Nets in Base 16

(125−101, 125, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 125, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 125, 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]

(125−101, 125, 129)-Net over F₁₆ — Digital

Digital (24, 125, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 125, 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]

(125−101, 125, 1230)-Net in Base 16 — Upper bound on s

There is no (24, 125, 1231)-net in base 16, because

1 times m-reduction [i] would yield (24, 124, 1231)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 207632 662031 605070 814517 289511 912797 480982 927539 189836 274574 983818 456403 322751 010943 326796 725185 220238 589951 945586 577623 561638 829792 760938 073511 423876 > 16¹²⁴ [i]