MinT - Best Known (47, 47+65, s)-Nets in Base 16

Best Known (47, 47+65, s)-Nets in Base 16

(47, 47+65, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 112, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 112, 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+65, 243)-Net over F₁₆ — Digital

Digital (47, 112, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 112, 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+65, 12793)-Net in Base 16 — Upper bound on s

There is no (47, 112, 12794)-net in base 16, because

1 times m-reduction [i] would yield (47, 111, 12794)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 45 507813 917707 910058 712961 235736 123159 861467 972967 889159 074439 608764 000959 681208 966757 162535 412931 454781 891072 738066 237582 831042 600121 > 16¹¹¹ [i]