MinT - Best Known (164−134, 164, s)-Nets in Base 8

Best Known (164−134, 164, s)-Nets in Base 8

(164−134, 164, 65)-Net over F₈ — Constructive and digital

Digital (30, 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]

(164−134, 164, 97)-Net over F₈ — Digital

Digital (30, 164, 97)-net over F₈, using

t-expansion [i] based on digital (28, 164, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(164−134, 164, 556)-Net in Base 8 — Upper bound on s

There is no (30, 164, 557)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13545 312243 372838 294707 134620 497756 684655 812095 659904 345110 179507 043106 676739 951123 257029 020181 895912 903869 747544 615340 567871 040333 198137 539379 960352 > 8¹⁶⁴ [i]