MinT - Best Known (42, 116, s)-Nets in Base 16

Best Known (42, 116, s)-Nets in Base 16

(42, 116, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 116, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 116, 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]

(42, 116, 5799)-Net in Base 16 — Upper bound on s

There is no (42, 116, 5800)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 866216 378795 465239 804273 786286 345801 709151 153569 191186 879955 128237 325104 642345 669374 499018 460118 364793 320020 017742 423850 917355 744776 252751 > 16¹¹⁶ [i]