MinT - Best Known (129−82, 129, s)-Nets in Base 16

Best Known (129−82, 129, s)-Nets in Base 16

(129−82, 129, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 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]

(129−82, 129, 243)-Net over F₁₆ — Digital

Digital (47, 129, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 129, 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]

(129−82, 129, 6590)-Net in Base 16 — Upper bound on s

There is no (47, 129, 6591)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 215563 090475 821859 423440 628543 270490 798615 374548 724019 838283 093163 126652 211715 405196 462063 599904 541643 420582 058386 866212 687256 344558 375537 153507 674415 822966 > 16¹²⁹ [i]