MinT - Best Known (30, 162, s)-Nets in Base 8

Best Known (30, 162, s)-Nets in Base 8

(30, 162, 65)-Net over F₈ — Constructive and digital

Digital (30, 162, 65)-net over F₈, using

t-expansion [i] based on digital (14, 162, 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]

(30, 162, 97)-Net over F₈ — Digital

Digital (30, 162, 97)-net over F₈, using

t-expansion [i] based on digital (28, 162, 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]

(30, 162, 556)-Net in Base 8 — Upper bound on s

There is no (30, 162, 557)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 202 294254 927809 027126 105852 502049 789136 523840 642504 578824 718268 093223 425614 466035 121187 685263 989399 088108 396537 738375 970128 040820 620492 789790 146640 > 8¹⁶² [i]