MinT - Best Known (52, 52+68, s)-Nets in Base 16

Best Known (52, 52+68, s)-Nets in Base 16

(52, 52+68, 243)-Net over F₁₆ — Constructive and digital

Digital (52, 120, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 120, 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]

(52, 52+68, 255)-Net over F₁₆ — Digital

Digital (52, 120, 255)-net over F₁₆, using

t-expansion [i] based on digital (50, 120, 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]

(52, 52+68, 257)-Net in Base 16

(52, 120, 257)-net in base 16, using

base change [i] based on digital (28, 96, 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]

(52, 52+68, 16021)-Net in Base 16 — Upper bound on s

There is no (52, 120, 16022)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 123110 033262 121474 360293 910794 803638 332163 848747 625849 292970 129516 651422 981499 336805 092226 358355 185274 092300 122988 694288 308520 642856 289799 653896 > 16¹²⁰ [i]