MinT - Best Known (43, 43+51, s)-Nets in Base 16

Best Known (43, 43+51, s)-Nets in Base 16

(43, 43+51, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 94, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 94, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(43, 43+51, 227)-Net over F₁₆ — Digital

Digital (43, 94, 227)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+51, 20444)-Net in Base 16 — Upper bound on s

There is no (43, 94, 20445)-net in base 16, because

1 times m-reduction [i] would yield (43, 93, 20445)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9628 701666 613769 353500 017029 031586 212256 472312 125051 556919 497438 107845 557451 709550 192981 287612 790857 519294 841876 > 16⁹³ [i]