MinT - Best Known (51, 51+71, s)-Nets in Base 16

Best Known (51, 51+71, s)-Nets in Base 16

(51, 51+71, 243)-Net over F₁₆ — Constructive and digital

Digital (51, 122, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 122, 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]

(51, 51+71, 255)-Net over F₁₆ — Digital

Digital (51, 122, 255)-net over F₁₆, using

t-expansion [i] based on digital (50, 122, 255)-net over F₁₆, using
- net from sequence [i] based on digital (50, 254)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 50 and N(F) ≥ 255, using
    - a curve from the manYPoints database [i]

(51, 51+71, 13469)-Net in Base 16 — Upper bound on s

There is no (51, 122, 13470)-net in base 16, because

1 times m-reduction [i] would yield (51, 121, 13470)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 49 959796 204900 037267 205938 043953 706781 092476 608781 465948 118090 318151 170965 910629 670427 934230 558607 406089 813381 187757 112208 606853 611486 797151 582376 > 16¹²¹ [i]