MinT - Best Known (111−58, 111, s)-Nets in Base 16

Best Known (111−58, 111, s)-Nets in Base 16

(111−58, 111, 243)-Net over F₁₆ — Constructive and digital

Digital (53, 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]

(111−58, 111, 313)-Net over F₁₆ — Digital

Digital (53, 111, 313)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−58, 111, 31599)-Net in Base 16 — Upper bound on s

There is no (53, 111, 31600)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 45 434012 662014 121547 397806 536360 894499 845036 307229 178421 638311 013719 223310 568980 877374 510604 281645 971540 918921 947761 375497 112194 166626 > 16¹¹¹ [i]