MinT - Best Known (50, 50+70, s)-Nets in Base 16

Best Known (50, 50+70, s)-Nets in Base 16

(50, 50+70, 243)-Net over F₁₆ — Constructive and digital

Digital (50, 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]

(50, 50+70, 255)-Net over F₁₆ — Digital

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]

(50, 50+70, 12442)-Net in Base 16 — Upper bound on s

There is no (50, 120, 12443)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 125575 575755 116930 177544 568582 191901 937251 774704 386683 445795 049141 091616 264929 284697 174850 730898 659243 747319 202822 346727 920208 190414 996940 284576 > 16¹²⁰ [i]