MinT - Best Known (74−56, 74, s)-Nets in Base 16

Best Known (74−56, 74, s)-Nets in Base 16

(74−56, 74, 65)-Net over F₁₆ — Constructive and digital

Digital (18, 74, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 74, 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]

(74−56, 74, 113)-Net over F₁₆ — Digital

Digital (18, 74, 113)-net over F₁₆, using

net from sequence [i] based on digital (18, 112)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 18 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(74−56, 74, 1130)-Net in Base 16 — Upper bound on s

There is no (18, 74, 1131)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 127916 117385 768568 029040 384683 392087 565722 108904 099865 383935 280165 878608 180340 942958 790696 > 16⁷⁴ [i]