MinT - Best Known (24, 113, s)-Nets in Base 16

Best Known (24, 113, s)-Nets in Base 16

(24, 113, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 113, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 113, 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]

(24, 113, 129)-Net over F₁₆ — Digital

Digital (24, 113, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 113, 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]

(24, 113, 1311)-Net in Base 16 — Upper bound on s

There is no (24, 113, 1312)-net in base 16, because

1 times m-reduction [i] would yield (24, 112, 1312)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 730 336652 999128 771861 156002 280038 420485 563845 586916 058948 301984 780704 165663 501828 556762 087541 995050 483932 362910 472425 032248 777236 569096 > 16¹¹² [i]