MinT - Best Known (6, 78, s)-Nets in Base 128

Best Known (6, 78, s)-Nets in Base 128

(6, 78, 216)-Net over F₁₂₈ — Constructive and digital

Digital (6, 78, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 78, 216)-net over F₁₂₈, using
- net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(6, 78, 243)-Net over F₁₂₈ — Digital

Digital (6, 78, 243)-net over F₁₂₈, using

net from sequence [i] based on digital (6, 242)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 6 and N(F) ≥ 243, using
  - a curve from the manYPoints database [i]

(6, 78, 4082)-Net in Base 128 — Upper bound on s

There is no (6, 78, 4083)-net in base 128, because

8 times m-reduction [i] would yield (6, 70, 4083)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 3208 937350 523383 052808 750261 967897 365727 720835 075961 295632 864714 021981 846841 251817 395621 629695 133775 120087 792030 175606 306270 648838 290938 611955 644565 > 128⁷⁰ [i]