MinT - Best Known (121−76, 121, s)-Nets in Base 16

Best Known (121−76, 121, s)-Nets in Base 16

(121−76, 121, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 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]

(121−76, 121, 242)-Net over F₁₆ — Digital

Digital (45, 121, 242)-net over F₁₆, using

net from sequence [i] based on digital (45, 241)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 45 and N(F) ≥ 242, using
  - a curve from the manYPoints database [i]

(121−76, 121, 6816)-Net in Base 16 — Upper bound on s

There is no (45, 121, 6817)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 152739 220971 392499 253415 654693 239727 156135 251994 833039 407747 004399 669213 316036 897208 828076 241930 208875 718990 230114 094842 612823 955350 501379 601216 > 16¹²¹ [i]