MinT - Best Known (122−81, 122, s)-Nets in Base 16

Best Known (122−81, 122, s)-Nets in Base 16

(122−81, 122, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 122, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 122, 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]

(122−81, 122, 4592)-Net in Base 16 — Upper bound on s

There is no (41, 122, 4593)-net in base 16, because

1 times m-reduction [i] would yield (41, 121, 4593)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 049694 027593 325808 829951 882779 626587 094025 357067 562196 716809 568623 181442 679239 034699 012603 567561 201658 860621 123856 390118 712843 896477 365467 356926 > 16¹²¹ [i]