MinT - Best Known (51, 111, s)-Nets in Base 16

Best Known (51, 111, s)-Nets in Base 16

(51, 111, 243)-Net over F₁₆ — Constructive and digital

Digital (51, 111, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 111, 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, 111, 266)-Net over F₁₆ — Digital

Digital (51, 111, 266)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 111, 22889)-Net in Base 16 — Upper bound on s

There is no (51, 111, 22890)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 45 481846 185442 103378 615644 167328 802046 200637 439684 636588 852767 501634 375947 663164 787438 676728 181791 302017 538487 642403 834596 845868 867376 > 16¹¹¹ [i]