MinT - Best Known (70, 70+76, s)-Nets in Base 8

Best Known (70, 70+76, s)-Nets in Base 8

(70, 70+76, 130)-Net over F₈ — Constructive and digital

Digital (70, 146, 130)-net over F₈, using

8 times m-reduction [i] based on digital (70, 154, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 56, 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, 98, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(70, 70+76, 203)-Net over F₈ — Digital

Digital (70, 146, 203)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+76, 6307)-Net in Base 8 — Upper bound on s

There is no (70, 146, 6308)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 713676 573660 128162 957104 323889 133591 830850 684862 002844 746417 704017 200336 376498 234639 440303 822900 583163 493685 193946 406754 666422 687072 > 8¹⁴⁶ [i]