MinT - Best Known (105−38, 105, s)-Nets in Base 16

Best Known (105−38, 105, s)-Nets in Base 16

(105−38, 105, 583)-Net over F₁₆ — Constructive and digital

Digital (67, 105, 583)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (6, 25, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]
2. digital (42, 80, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 40, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(105−38, 105, 2571)-Net over F₁₆ — Digital

Digital (67, 105, 2571)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−38, 105, 2384897)-Net in Base 16 — Upper bound on s

There is no (67, 105, 2384898)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 707704 089792 923581 012628 861507 627485 337719 418042 256304 761598 990793 142369 621425 815837 507853 344484 404317 586060 814601 485399 430656 > 16¹⁰⁵ [i]