MinT - Best Known (129−84, 129, s)-Nets in Base 16

Best Known (129−84, 129, s)-Nets in Base 16

(129−84, 129, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 129, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 129, 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]

(129−84, 129, 242)-Net over F₁₆ — Digital

Digital (45, 129, 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]

(129−84, 129, 5473)-Net in Base 16 — Upper bound on s

There is no (45, 129, 5474)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 215948 340085 526786 838455 489393 990677 162129 297424 214945 637966 682889 417452 767599 900889 461746 985292 004098 084626 865142 296532 068852 869026 439395 978946 904958 790496 > 16¹²⁹ [i]