MinT - Best Known (162−124, 162, s)-Nets in Base 8

Best Known (162−124, 162, s)-Nets in Base 8

(162−124, 162, 98)-Net over F₈ — Constructive and digital

Digital (38, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(162−124, 162, 129)-Net over F₈ — Digital

Digital (38, 162, 129)-net over F₈, using

net from sequence [i] based on digital (38, 128)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(162−124, 162, 743)-Net in Base 8 — Upper bound on s

There is no (38, 162, 744)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 201 150101 406275 370049 728211 940581 148980 503752 997550 140201 947410 786289 240499 224940 202640 388620 433809 650912 833174 462571 973732 140113 954974 873531 489624 > 8¹⁶² [i]