MinT - Best Known (25, 62, s)-Nets in Base 16

Best Known (25, 62, s)-Nets in Base 16

(25, 62, 89)-Net over F₁₆ — Constructive and digital

Digital (25, 62, 89)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (1, 19, 24)-net over F₁₆, using
  - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. digital (6, 43, 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]

(25, 62, 120)-Net in Base 16 — Constructive

(25, 62, 120)-net in base 16, using

8 times m-reduction [i] based on (25, 70, 120)-net in base 16, using
- base change [i] based on digital (11, 56, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(25, 62, 144)-Net over F₁₆ — Digital

Digital (25, 62, 144)-net over F₁₆, using

net from sequence [i] based on digital (25, 143)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 25 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(25, 62, 6053)-Net in Base 16 — Upper bound on s

There is no (25, 62, 6054)-net in base 16, because

1 times m-reduction [i] would yield (25, 61, 6054)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 28 351444 326748 775891 084884 054756 342943 499105 369287 936887 132667 469359 966956 > 16⁶¹ [i]