MinT - Best Known (70, 70+72, s)-Nets in Base 8

Best Known (70, 70+72, s)-Nets in Base 8

(70, 70+72, 130)-Net over F₈ — Constructive and digital

Digital (70, 142, 130)-net over F₈, using

12 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+72, 220)-Net over F₈ — Digital

Digital (70, 142, 220)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+72, 7421)-Net in Base 8 — Upper bound on s

There is no (70, 142, 7422)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 511938 947435 398358 534517 892655 403070 310497 646641 222076 605041 699843 198860 189428 023260 333291 433576 911255 097929 328922 431949 463575 > 8¹⁴² [i]