MinT - Best Known (164−110, 164, s)-Nets in Base 8

Best Known (164−110, 164, s)-Nets in Base 8

(164−110, 164, 98)-Net over F₈ — Constructive and digital

Digital (54, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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]

(164−110, 164, 144)-Net over F₈ — Digital

Digital (54, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(164−110, 164, 1468)-Net in Base 8 — Upper bound on s

There is no (54, 164, 1469)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13158 884162 043079 780650 893495 370913 859711 736720 181461 850112 682283 860539 059508 357705 706559 703513 986984 369791 240078 626429 703966 840260 585871 466439 717688 > 8¹⁶⁴ [i]