MinT - Best Known (56, 56+66, s)-Nets in Base 16

Best Known (56, 56+66, s)-Nets in Base 16

(56, 56+66, 243)-Net over F₁₆ — Constructive and digital

Digital (56, 122, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 122, 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]

(56, 56+66, 286)-Net over F₁₆ — Digital

Digital (56, 122, 286)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+66, 24805)-Net in Base 16 — Upper bound on s

There is no (56, 122, 24806)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 800 216617 770389 628589 268432 584048 606645 791433 943033 601343 107339 078419 661837 684396 882834 018104 714197 089482 630836 329717 949000 713810 756166 467220 061521 > 16¹²² [i]