MinT - Best Known (121−77, 121, s)-Nets in Base 16

Best Known (121−77, 121, s)-Nets in Base 16

(121−77, 121, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 121, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 121, 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]

(121−77, 121, 226)-Net over F₁₆ — Digital

Digital (44, 121, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 121, 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]

(121−77, 121, 6335)-Net in Base 16 — Upper bound on s

There is no (44, 121, 6336)-net in base 16, because

1 times m-reduction [i] would yield (44, 120, 6336)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 137422 586174 375127 875929 004817 324447 038768 326386 040435 229131 964783 918101 279412 019567 452436 285596 931136 132409 523332 809584 642465 682191 741917 840071 > 16¹²⁰ [i]