MinT - Best Known (55, 55+67, s)-Nets in Base 16

Best Known (55, 55+67, s)-Nets in Base 16

(55, 55+67, 243)-Net over F₁₆ — Constructive and digital

Digital (55, 122, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 122, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(55, 55+67, 273)-Net over F₁₆ — Digital

Digital (55, 122, 273)-net over F₁₆, using

net from sequence [i] based on digital (55, 272)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 55 and N(F) ≥ 273, using
  - Drinfeld modules of rank 1 [i]

(55, 55+67, 22804)-Net in Base 16 — Upper bound on s

There is no (55, 122, 22805)-net in base 16, because

1 times m-reduction [i] would yield (55, 121, 22805)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 49 974593 499356 221826 771634 613472 936881 516371 851739 026869 979287 907228 663974 238766 946047 622772 095893 173552 526916 606218 973276 433324 101415 624984 442976 > 16¹²¹ [i]