MinT - Best Known (120−77, 120, s)-Nets in Base 16

Best Known (120−77, 120, s)-Nets in Base 16

(120−77, 120, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 120, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 120, 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]

(120−77, 120, 226)-Net over F₁₆ — Digital

Digital (43, 120, 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]

(120−77, 120, 5887)-Net in Base 16 — Upper bound on s

There is no (43, 120, 5888)-net in base 16, because

1 times m-reduction [i] would yield (43, 119, 5888)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 195218 107270 733078 585486 425391 072539 887612 612878 144625 146778 438739 219657 173757 043374 508221 184939 224531 741597 309020 679426 257971 757285 486257 991961 > 16¹¹⁹ [i]