MinT - Best Known (70, 70+79, s)-Nets in Base 8

Best Known (70, 70+79, s)-Nets in Base 8

(70, 70+79, 130)-Net over F₈ — Constructive and digital

Digital (70, 149, 130)-net over F₈, using

5 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+79, 192)-Net over F₈ — Digital

Digital (70, 149, 192)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+79, 5856)-Net in Base 8 — Upper bound on s

There is no (70, 149, 5857)-net in base 8, because

1 times m-reduction [i] would yield (70, 148, 5857)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 644667 638626 229051 589750 410757 160870 368244 991156 390996 608325 221007 591475 974774 322377 123516 523409 163983 910296 371178 377339 450934 498112 > 8¹⁴⁸ [i]