MinT - Best Known (76, 76+44, s)-Nets in Base 16

Best Known (76, 76+44, s)-Nets in Base 16

(76, 76+44, 583)-Net over F₁₆ — Constructive and digital

Digital (76, 120, 583)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (6, 28, 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 (48, 92, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 46, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(76, 76+44, 2602)-Net over F₁₆ — Digital

Digital (76, 120, 2602)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+44, 2231961)-Net in Base 16 — Upper bound on s

There is no (76, 120, 2231962)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 121776 819935 655452 130346 611946 661105 984145 674642 662867 067691 317588 260609 274021 616434 860819 349666 756634 319522 070567 580803 763163 573742 422524 244636 > 16¹²⁰ [i]