MinT - Best Known (107−63, 107, s)-Nets in Base 16

Best Known (107−63, 107, s)-Nets in Base 16

(107−63, 107, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 107, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 107, 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]

(107−63, 107, 226)-Net over F₁₆ — Digital

Digital (44, 107, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 107, 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]

(107−63, 107, 10828)-Net in Base 16 — Upper bound on s

There is no (44, 107, 10829)-net in base 16, because

1 times m-reduction [i] would yield (44, 106, 10829)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 374977 215350 010497 197685 114724 518988 506692 191905 004314 270724 668438 009876 638981 761582 856553 970383 249782 304542 152125 109802 556736 > 16¹⁰⁶ [i]