MinT - Best Known (97−51, 97, s)-Nets in Base 16

Best Known (97−51, 97, s)-Nets in Base 16

(97−51, 97, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 97, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 97, 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]

(97−51, 97, 272)-Net over F₁₆ — Digital

Digital (46, 97, 272)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−51, 97, 28519)-Net in Base 16 — Upper bound on s

There is no (46, 97, 28520)-net in base 16, because

1 times m-reduction [i] would yield (46, 96, 28520)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 407125 134924 287261 890398 945888 101410 193999 237590 865490 275168 801953 825594 044537 122301 978541 748490 076785 363678 916876 > 16⁹⁶ [i]