MinT - Best Known (24, 62, s)-Nets in Base 16

Best Known (24, 62, s)-Nets in Base 16

(24, 62, 71)-Net over F₁₆ — Constructive and digital

Digital (24, 62, 71)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 21, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. digital (3, 41, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(24, 62, 120)-Net in Base 16 — Constructive

(24, 62, 120)-net in base 16, using

3 times m-reduction [i] based on (24, 65, 120)-net in base 16, using
- base change [i] based on digital (11, 52, 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]

(24, 62, 129)-Net over F₁₆ — Digital

Digital (24, 62, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 62, 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]

(24, 62, 4480)-Net in Base 16 — Upper bound on s

There is no (24, 62, 4481)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 452 518347 496235 821496 727644 641843 740833 574178 060489 369433 859623 609877 847936 > 16⁶² [i]