MinT - Best Known (46, 46+67, s)-Nets in Base 16

Best Known (46, 46+67, s)-Nets in Base 16

(46, 46+67, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 113, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 113, 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]

(46, 46+67, 243)-Net over F₁₆ — Digital

Digital (46, 113, 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]

(46, 46+67, 10696)-Net in Base 16 — Upper bound on s

There is no (46, 113, 10697)-net in base 16, because

1 times m-reduction [i] would yield (46, 112, 10697)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 728 324323 495187 072064 048925 242493 718541 498163 073315 854751 273032 604871 227993 230510 872504 088590 600812 715105 755297 215175 153932 014373 262416 > 16¹¹² [i]