MinT - Best Known (45, 45+46, s)-Nets in Base 16

Best Known (45, 45+46, s)-Nets in Base 16

(45, 45+46, 257)-Net over F₁₆ — Constructive and digital

Digital (45, 91, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(45,256) in PG(90,16)) for nets [i] based on digital (0, 46, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(45, 45+46, 315)-Net over F₁₆ — Digital

Digital (45, 91, 315)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+46, 36504)-Net in Base 16 — Upper bound on s

There is no (45, 91, 36505)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 37 595617 348318 162661 837558 927593 774266 553494 064768 584349 357879 973601 872070 072111 555868 018953 759121 122150 159976 > 16⁹¹ [i]