MinT - Best Known (19, 19+83, s)-Nets in Base 16

Best Known (19, 19+83, s)-Nets in Base 16

(19, 19+83, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 102, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 102, 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]

(19, 19+83, 129)-Net over F₁₆ — Digital

Digital (19, 102, 129)-net over F₁₆, using

net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(19, 19+83, 972)-Net in Base 16 — Upper bound on s

There is no (19, 102, 973)-net in base 16, because

1 times m-reduction [i] would yield (19, 101, 973)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 389291 070489 185690 708466 150753 943431 395215 183927 455278 213503 335507 723335 631241 506627 031486 596876 826124 861142 086416 857896 > 16¹⁰¹ [i]