MinT - Best Known (76, 76+80, s)-Nets in Base 8

Best Known (76, 76+80, s)-Nets in Base 8

(76, 76+80, 130)-Net over F₈ — Constructive and digital

Digital (76, 156, 130)-net over F₈, using

16 times m-reduction [i] based on digital (76, 172, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 62, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]
  2. digital (14, 110, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(76, 76+80, 228)-Net over F₈ — Digital

Digital (76, 156, 228)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+80, 7469)-Net in Base 8 — Upper bound on s

There is no (76, 156, 7470)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 764 854425 968110 152616 131707 420672 672835 855666 223912 849282 262246 537072 756922 815499 526242 007203 199749 647953 223410 972725 569817 130393 607096 668455 > 8¹⁵⁶ [i]