MinT - Best Known (71−59, 71, s)-Nets in Base 16

Best Known (71−59, 71, s)-Nets in Base 16

(71−59, 71, 65)-Net over F₁₆ — Constructive and digital

Digital (12, 71, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 71, 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]

(71−59, 71, 88)-Net over F₁₆ — Digital

Digital (12, 71, 88)-net over F₁₆, using

net from sequence [i] based on digital (12, 87)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 12 and N(F) ≥ 88, using
  - a curve from the manYPoints database [i]

(71−59, 71, 611)-Net in Base 16 — Upper bound on s

There is no (12, 71, 612)-net in base 16, because

1 times m-reduction [i] would yield (12, 70, 612)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 984149 165932 791576 185813 557607 664185 181316 832826 660478 860769 276400 264881 496086 939896 > 16⁷⁰ [i]