MinT - Best Known (44, 44+59, s)-Nets in Base 16

Best Known (44, 44+59, s)-Nets in Base 16

(44, 44+59, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 103, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 103, 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]

(44, 44+59, 226)-Net over F₁₆ — Digital

Digital (44, 103, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 103, 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]

(44, 44+59, 13356)-Net in Base 16 — Upper bound on s

There is no (44, 103, 13357)-net in base 16, because

1 times m-reduction [i] would yield (44, 102, 13357)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 661 724025 929139 759646 737302 287701 241847 169460 904144 672256 780915 936055 372607 005802 905266 508441 887034 924445 447454 533358 052096 > 16¹⁰² [i]