MinT - Best Known (19, 19+111, s)-Nets in Base 16

Best Known (19, 19+111, s)-Nets in Base 16

(19, 19+111, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 130, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 130, 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+111, 129)-Net over F₁₆ — Digital

Digital (19, 130, 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+111, 918)-Net in Base 16 — Upper bound on s

There is no (19, 130, 919)-net in base 16, because

1 times m-reduction [i] would yield (19, 129, 919)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 219621 705008 285806 985470 110467 025867 325167 818984 966603 087603 701690 020769 993208 211209 476827 955184 780413 953400 523236 398374 506884 252392 601943 938201 130163 498176 > 16¹²⁹ [i]