MinT - Best Known (109−65, 109, s)-Nets in Base 16

Best Known (109−65, 109, s)-Nets in Base 16

(109−65, 109, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 109, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 109, 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]

(109−65, 109, 226)-Net over F₁₆ — Digital

Digital (44, 109, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 109, 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]

(109−65, 109, 9860)-Net in Base 16 — Upper bound on s

There is no (44, 109, 9861)-net in base 16, because

1 times m-reduction [i] would yield (44, 108, 9861)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11092 697400 407305 660123 337628 705928 022127 704517 646771 005262 989640 810379 579476 822345 816262 140571 983105 792603 933920 547435 880588 575756 > 16¹⁰⁸ [i]