MinT - Best Known (163−122, 163, s)-Nets in Base 8

Best Known (163−122, 163, s)-Nets in Base 8

(163−122, 163, 98)-Net over F₈ — Constructive and digital

Digital (41, 163, 98)-net over F₈, using

t-expansion [i] based on digital (37, 163, 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]

(163−122, 163, 129)-Net over F₈ — Digital

Digital (41, 163, 129)-net over F₈, using

t-expansion [i] based on digital (38, 163, 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]

(163−122, 163, 833)-Net in Base 8 — Upper bound on s

There is no (41, 163, 834)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1671 726733 498364 221595 739341 065376 751599 917890 673699 419733 522894 150740 361801 713936 085298 846304 754254 146699 768222 479128 741054 803528 327802 590342 353808 > 8¹⁶³ [i]