MinT - Best Known (52, 52+59, s)-Nets in Base 16

Best Known (52, 52+59, s)-Nets in Base 16

(52, 52+59, 243)-Net over F₁₆ — Constructive and digital

Digital (52, 111, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 111, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(52, 52+59, 288)-Net over F₁₆ — Digital

Digital (52, 111, 288)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+59, 28717)-Net in Base 16 — Upper bound on s

There is no (52, 111, 28718)-net in base 16, because

1 times m-reduction [i] would yield (52, 110, 28718)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 841607 122043 075711 816305 350432 896294 747849 587051 745924 700567 452123 425346 729921 933139 872305 655279 785126 200498 465945 186348 662582 988806 > 16¹¹⁰ [i]