MinT - Best Known (52−41, 52, s)-Nets in Base 16

Best Known (52−41, 52, s)-Nets in Base 16

(52−41, 52, 65)-Net over F₁₆ — Constructive and digital

Digital (11, 52, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 52, 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]

(52−41, 52, 81)-Net over F₁₆ — Digital

Digital (11, 52, 81)-net over F₁₆, using

t-expansion [i] based on digital (10, 52, 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]

(52−41, 52, 640)-Net in Base 16 — Upper bound on s

There is no (11, 52, 641)-net in base 16, because

1 times m-reduction [i] would yield (11, 51, 641)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 26 170895 540045 970414 905132 168846 973828 486379 704576 377467 838176 > 16⁵¹ [i]