MinT - Best Known (65−58, 65, s)-Nets in Base 16

Best Known (65−58, 65, s)-Nets in Base 16

(65−58, 65, 65)-Net over F₁₆ — Constructive and digital

Digital (7, 65, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 65, 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]

(65−58, 65, 361)-Net in Base 16 — Upper bound on s

There is no (7, 65, 362)-net in base 16, because

12 times m-reduction [i] would yield (7, 53, 362)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6684 408024 466728 093536 660646 380472 079625 367637 738874 536220 735416 > 16⁵³ [i]