MinT - Best Known (71, 71+98, s)-Nets in Base 8

Best Known (71, 71+98, s)-Nets in Base 8

(71, 71+98, 100)-Net over F₈ — Constructive and digital

Digital (71, 169, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 57, 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, 112, 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]

(71, 71+98, 150)-Net over F₈ — Digital

Digital (71, 169, 150)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+98, 156)-Net in Base 8

(71, 169, 156)-net in base 8, using

t-expansion [i] based on (70, 169, 156)-net in base 8, using
- 3 times m-reduction [i] based on (70, 172, 156)-net in base 8, using
  - base change [i] based on digital (27, 129, 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]

(71, 71+98, 3524)-Net in Base 8 — Upper bound on s

There is no (71, 169, 3525)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 419 117069 877458 071281 061650 768616 558681 517564 937285 166992 199744 992297 461604 566323 221994 421946 176436 460271 728027 005838 365121 016977 973027 824140 750531 726288 > 8¹⁶⁹ [i]