MinT - Best Known (115−42, 115, s)-Nets in Base 16

Best Known (115−42, 115, s)-Nets in Base 16

(115−42, 115, 583)-Net over F₁₆ — Constructive and digital

Digital (73, 115, 583)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (6, 27, 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 (46, 88, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 44, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(115−42, 115, 2586)-Net over F₁₆ — Digital

Digital (73, 115, 2586)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−42, 115, 2271901)-Net in Base 16 — Upper bound on s

There is no (73, 115, 2271902)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 977143 462743 375092 668973 209075 982388 235316 952888 103129 926655 309656 990403 553795 894475 520191 579704 759261 840159 504581 203376 318466 792994 064631 > 16¹¹⁵ [i]