MinT - Best Known (66, 105, s)-Nets in Base 16

Best Known (66, 105, s)-Nets in Base 16

(66, 105, 581)-Net over F₁₆ — Constructive and digital

Digital (66, 105, 581)-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 (41, 80, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 40, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(66, 105, 2147)-Net over F₁₆ — Digital

Digital (66, 105, 2147)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 105, 2061078)-Net in Base 16 — Upper bound on s

There is no (66, 105, 2061079)-net in base 16, because

1 times m-reduction [i] would yield (66, 104, 2061079)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 169230 459044 197895 107893 860113 934420 957837 848965 194064 471988 071905 618293 308966 247836 812506 034581 422282 943681 928488 339638 133516 > 16¹⁰⁴ [i]