MinT - Best Known (43, 99, s)-Nets in Base 16

Best Known (43, 99, s)-Nets in Base 16

(43, 99, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 99, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 99, 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, 99, 226)-Net over F₁₆ — Digital

Digital (43, 99, 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, 99, 13609)-Net in Base 16 — Upper bound on s

There is no (43, 99, 13610)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 161495 373509 695055 487345 580165 678323 009165 547023 110713 280832 877658 153614 889026 527678 069100 715700 033406 282060 383830 029576 > 16⁹⁹ [i]