MinT - Best Known (13, 13+67, s)-Nets in Base 16

Best Known (13, 13+67, s)-Nets in Base 16

(13, 13+67, 65)-Net over F₁₆ — Constructive and digital

Digital (13, 80, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 80, 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]

(13, 13+67, 97)-Net over F₁₆ — Digital

Digital (13, 80, 97)-net over F₁₆, using

net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
  - a curve from the manYPoints database [i]

(13, 13+67, 651)-Net in Base 16 — Upper bound on s

There is no (13, 80, 652)-net in base 16, because

1 times m-reduction [i] would yield (13, 79, 652)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 136284 696989 592853 151560 430594 338025 791233 837163 094817 365262 387499 928066 392735 780030 393163 869516 > 16⁷⁹ [i]