MinT - Best Known (43, 43+71, s)-Nets in Base 16

Best Known (43, 43+71, s)-Nets in Base 16

(43, 43+71, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 114, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 114, 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]

(43, 43+71, 226)-Net over F₁₆ — Digital

Digital (43, 114, 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]

(43, 43+71, 7138)-Net in Base 16 — Upper bound on s

There is no (43, 114, 7139)-net in base 16, because

1 times m-reduction [i] would yield (43, 113, 7139)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11677 527078 426374 699107 805022 943672 891557 926692 620055 029946 044570 551431 696221 896469 325592 785892 945772 030326 164074 235387 753316 365676 832976 > 16¹¹³ [i]