MinT - Best Known (127−81, 127, s)-Nets in Base 16

Best Known (127−81, 127, s)-Nets in Base 16

(127−81, 127, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 127, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 127, 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]

(127−81, 127, 243)-Net over F₁₆ — Digital

Digital (46, 127, 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]

(127−81, 127, 6504)-Net in Base 16 — Upper bound on s

There is no (46, 127, 6505)-net in base 16, because

1 times m-reduction [i] would yield (46, 126, 6505)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 594902 007253 317797 013530 849270 333106 221327 030326 289454 550385 754830 086890 102563 104930 597654 518818 557519 707117 184579 562910 967903 507424 094714 864533 216751 > 16¹²⁶ [i]