MinT - Best Known (47, 47+69, s)-Nets in Base 16

Best Known (47, 47+69, s)-Nets in Base 16

(47, 47+69, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 116, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 116, 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]

(47, 47+69, 243)-Net over F₁₆ — Digital

Digital (47, 116, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 116, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(47, 47+69, 10650)-Net in Base 16 — Upper bound on s

There is no (47, 116, 10651)-net in base 16, because

1 times m-reduction [i] would yield (47, 115, 10651)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 979848 227203 154264 897936 202181 329090 644877 165033 847705 709889 871544 169545 077817 394386 789156 445880 100599 497208 370273 539013 880766 552330 674236 > 16¹¹⁵ [i]