MinT - Best Known (35, 125, s)-Nets in Base 16

Best Known (35, 125, s)-Nets in Base 16

(35, 125, 65)-Net over F₁₆ — Constructive and digital

Digital (35, 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]

(35, 125, 104)-Net in Base 16 — Constructive

(35, 125, 104)-net in base 16, using

5 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- base change [i] based on digital (9, 104, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(35, 125, 193)-Net over F₁₆ — Digital

Digital (35, 125, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 125, 193)-net over F₁₆, using
- net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
    - a curve from the manYPoints database [i]

(35, 125, 2574)-Net in Base 16 — Upper bound on s

There is no (35, 125, 2575)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 308638 847209 571831 927937 794768 806644 597914 766497 234242 345330 337692 740853 597948 277558 726810 304536 241946 915713 893960 903464 962072 289672 039175 647193 169376 > 16¹²⁵ [i]