MinT - Best Known (50, 50+72, s)-Nets in Base 16

Best Known (50, 50+72, s)-Nets in Base 16

(50, 50+72, 243)-Net over F₁₆ — Constructive and digital

Digital (50, 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]

(50, 50+72, 255)-Net over F₁₆ — Digital

Digital (50, 122, 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+72, 11442)-Net in Base 16 — Upper bound on s

There is no (50, 122, 11443)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 800 461717 037545 443996 231901 353130 473282 573669 775663 383583 684664 558191 828651 773276 069844 621640 953522 949923 229381 291414 492262 412802 336140 364474 621596 > 16¹²² [i]