MinT - Best Known (117−71, 117, s)-Nets in Base 16

Best Known (117−71, 117, s)-Nets in Base 16

(117−71, 117, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 117, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 117, 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]

(117−71, 117, 243)-Net over F₁₆ — Digital

Digital (46, 117, 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]

(117−71, 117, 9058)-Net in Base 16 — Upper bound on s

There is no (46, 117, 9059)-net in base 16, because

1 times m-reduction [i] would yield (46, 116, 9059)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 770368 417801 547957 777229 206084 056776 456084 440314 642316 486217 742835 302164 913282 588546 942987 851736 529366 394198 800562 050620 845966 932810 920976 > 16¹¹⁶ [i]