MinT - Best Known (111−70, 111, s)-Nets in Base 16

Best Known (111−70, 111, s)-Nets in Base 16

(111−70, 111, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 111, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 111, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(111−70, 111, 6089)-Net in Base 16 — Upper bound on s

There is no (41, 111, 6090)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 45 572956 447138 113596 698589 442549 689086 024251 351206 735518 895211 743036 244382 740117 318934 716846 284462 694801 663641 772894 942775 787634 840376 > 16¹¹¹ [i]