MinT - Best Known (52−37, 52, s)-Nets in Base 16

Best Known (52−37, 52, s)-Nets in Base 16

(52−37, 52, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 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]

(52−37, 52, 98)-Net over F₁₆ — Digital

Digital (15, 52, 98)-net over F₁₆, using

net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(52−37, 52, 1289)-Net in Base 16 — Upper bound on s

There is no (15, 52, 1290)-net in base 16, because

1 times m-reduction [i] would yield (15, 51, 1290)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 25 844336 198744 002709 127809 036217 978793 497717 917298 325213 706176 > 16⁵¹ [i]