MinT - Best Known (127−84, 127, s)-Nets in Base 16

Best Known (127−84, 127, s)-Nets in Base 16

(127−84, 127, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 127, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 127, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(127−84, 127, 226)-Net over F₁₆ — Digital

Digital (43, 127, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(127−84, 127, 4793)-Net in Base 16 — Upper bound on s

There is no (43, 127, 4794)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 842 954358 796965 686153 462323 516746 438459 778550 462966 733134 807302 134487 139194 310961 335704 465245 959145 189540 804376 838539 186447 201819 808975 895109 521262 861096 > 16¹²⁷ [i]