MinT - Best Known (51, 113, s)-Nets in Base 16

Best Known (51, 113, s)-Nets in Base 16

(51, 113, 243)-Net over F₁₆ — Constructive and digital

Digital (51, 113, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 113, 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]

(51, 113, 255)-Net over F₁₆ — Digital

Digital (51, 113, 255)-net over F₁₆, using

t-expansion [i] based on digital (50, 113, 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]

(51, 113, 257)-Net in Base 16

(51, 113, 257)-net in base 16, using

2 times m-reduction [i] based on (51, 115, 257)-net in base 16, using
- base change [i] based on digital (28, 92, 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]

(51, 113, 20266)-Net in Base 16 — Upper bound on s

There is no (51, 113, 20267)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11630 831889 183202 457073 250325 995332 222194 851817 411573 010379 033647 954035 097423 082327 821839 287719 964966 706675 627343 970181 489747 567689 898656 > 16¹¹³ [i]