MinT - Best Known (121−74, 121, s)-Nets in Base 16

Best Known (121−74, 121, s)-Nets in Base 16

(121−74, 121, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 121, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 121, 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]

(121−74, 121, 243)-Net over F₁₆ — Digital

Digital (47, 121, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 121, 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]

(121−74, 121, 8444)-Net in Base 16 — Upper bound on s

There is no (47, 121, 8445)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 084088 679662 372631 091682 883832 603434 664330 116769 290062 356646 909369 620922 108021 224820 610993 164358 143869 957568 143755 588390 998869 774514 369996 507976 > 16¹²¹ [i]