MinT - Best Known (50, 78, s)-Nets in Base 16

Best Known (50, 78, s)-Nets in Base 16

(50, 78, 581)-Net over F₁₆ — Constructive and digital

Digital (50, 78, 581)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (6, 20, 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 (30, 58, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 29, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(50, 78, 2206)-Net over F₁₆ — Digital

Digital (50, 78, 2206)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 78, 2060788)-Net in Base 16 — Upper bound on s

There is no (50, 78, 2060789)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8343 736708 369620 901653 690712 347967 603410 639832 989164 562515 408121 284617 714873 521353 318418 661816 > 16⁷⁸ [i]