MinT - Best Known (115−71, 115, s)-Nets in Base 16

Best Known (115−71, 115, s)-Nets in Base 16

(115−71, 115, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 115, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 115, 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]

(115−71, 115, 226)-Net over F₁₆ — Digital

Digital (44, 115, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 115, 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]

(115−71, 115, 7728)-Net in Base 16 — Upper bound on s

There is no (44, 115, 7729)-net in base 16, because

1 times m-reduction [i] would yield (44, 114, 7729)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 186736 048223 120364 597886 162164 790664 948686 753427 541426 696227 415437 792419 475176 177916 017459 113290 835133 601126 280993 832063 973732 285918 508976 > 16¹¹⁴ [i]