MinT - Best Known (68, 160, s)-Nets in Base 8

Best Known (68, 160, s)-Nets in Base 8

(68, 160, 100)-Net over F₈ — Constructive and digital

Digital (68, 160, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 54, 35)-net over F₈, using
  - net from sequence [i] based on digital (8, 34)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 7, N(F)Â =Â 34, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using a function field by SÃ©mirat [i]
2. digital (14, 106, 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]

(68, 160, 148)-Net over F₈ — Digital

Digital (68, 160, 148)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 160, 156)-Net in Base 8

(68, 160, 156)-net in base 8, using

4 times m-reduction [i] based on (68, 164, 156)-net in base 8, using
- base change [i] based on digital (27, 123, 156)-net over F₁₆, using
  - net from sequence [i] based on digital (27, 155)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 27 and N(F) ≥ 156, using
      - a curve from the manYPoints database [i]

(68, 160, 3529)-Net in Base 8 — Upper bound on s

There is no (68, 160, 3530)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 126255 287376 562400 425803 028522 187034 655690 403424 516188 360049 137672 000227 581861 609369 312394 265016 426211 965492 477226 977102 446938 739542 736241 791520 > 8¹⁶⁰ [i]