MinT - Best Known (10, 25, s)-Nets in Base 16

Best Known (10, 25, s)-Nets in Base 16

(10, 25, 65)-Net over F₁₆ — Constructive and digital

Digital (10, 25, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 25, 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]

(10, 25, 80)-Net in Base 16 — Constructive

(10, 25, 80)-net in base 16, using

2 times m-reduction [i] based on (10, 27, 80)-net in base 16, using
- base change [i] based on digital (1, 18, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(10, 25, 81)-Net over F₁₆ — Digital

Digital (10, 25, 81)-net over F₁₆, using

net from sequence [i] based on digital (10, 80)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 10 and N(F) ≥ 81, using
  - a curve from the manYPoints database [i]

(10, 25, 83)-Net in Base 16

(10, 25, 83)-net in base 16, using

base change [i] based on digital (5, 20, 83)-net over F₃₂, using
- net from sequence [i] based on digital (5, 82)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 83, using
    - a curve from the manYPoints database [i]

(10, 25, 3025)-Net in Base 16 — Upper bound on s

There is no (10, 25, 3026)-net in base 16, because

1 times m-reduction [i] would yield (10, 24, 3026)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 79390 834727 079415 134910 372456 > 16²⁴ [i]