MinT - Best Known (123−77, 123, s)-Nets in Base 16

Best Known (123−77, 123, s)-Nets in Base 16

(123−77, 123, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 123, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 123, 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]

(123−77, 123, 243)-Net over F₁₆ — Digital

Digital (46, 123, 243)-net over F₁₆, using

net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
  - a curve from the manYPoints database [i]

(123−77, 123, 7333)-Net in Base 16 — Upper bound on s

There is no (46, 123, 7334)-net in base 16, because

1 times m-reduction [i] would yield (46, 122, 7334)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 800 074319 959584 554835 505914 348739 788275 234787 478170 005037 736794 713569 353772 094773 098593 832915 354631 852955 769097 639031 840543 281507 487946 782418 828256 > 16¹²² [i]