MinT - Best Known (164−128, 164, s)-Nets in Base 8

Best Known (164−128, 164, s)-Nets in Base 8

(164−128, 164, 65)-Net over F₈ — Constructive and digital

Digital (36, 164, 65)-net over F₈, using

t-expansion [i] based on digital (14, 164, 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]

(164−128, 164, 112)-Net over F₈ — Digital

Digital (36, 164, 112)-net over F₈, using

t-expansion [i] based on digital (35, 164, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(164−128, 164, 686)-Net in Base 8 — Upper bound on s

There is no (36, 164, 687)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13181 258712 276601 782602 902940 014530 347774 105435 934291 735641 553893 039373 541981 342954 709907 972379 466320 104627 761896 841205 426252 287835 717157 896767 585418 > 8¹⁶⁴ [i]