MinT - Best Known (53, 53+72, s)-Nets in Base 16

Best Known (53, 53+72, s)-Nets in Base 16

(53, 53+72, 243)-Net over F₁₆ — Constructive and digital

Digital (53, 125, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 125, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(53, 53+72, 255)-Net over F₁₆ — Digital

Digital (53, 125, 255)-net over F₁₆, using

t-expansion [i] based on digital (50, 125, 255)-net over F₁₆, using
- net from sequence [i] based on digital (50, 254)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 50 and N(F) ≥ 255, using
    - a curve from the manYPoints database [i]

(53, 53+72, 257)-Net in Base 16

(53, 125, 257)-net in base 16, using

base change [i] based on digital (28, 100, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(53, 53+72, 14421)-Net in Base 16 — Upper bound on s

There is no (53, 125, 14422)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 275056 391343 745235 872212 531020 499850 094290 286949 459752 087643 153760 216854 116267 734089 288594 463872 478519 667099 848829 636241 430450 354069 275954 738634 037506 > 16¹²⁵ [i]