MinT - Best Known (53−41, 53, s)-Nets in Base 16

Best Known (53−41, 53, s)-Nets in Base 16

(53−41, 53, 65)-Net over F₁₆ — Constructive and digital

Digital (12, 53, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 53, 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]

(53−41, 53, 88)-Net over F₁₆ — Digital

Digital (12, 53, 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]

(53−41, 53, 737)-Net in Base 16 — Upper bound on s

There is no (12, 53, 738)-net in base 16, because

1 times m-reduction [i] would yield (12, 52, 738)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 419 699998 749844 984549 476860 189581 817451 391631 646420 992782 814776 > 16⁵² [i]