MinT - Best Known (169−114, 169, s)-Nets in Base 8

Best Known (169−114, 169, s)-Nets in Base 8

(169−114, 169, 98)-Net over F₈ — Constructive and digital

Digital (55, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(169−114, 169, 144)-Net over F₈ — Digital

Digital (55, 169, 144)-net over F₈, using

t-expansion [i] based on digital (45, 169, 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]

(169−114, 169, 1465)-Net in Base 8 — Upper bound on s

There is no (55, 169, 1466)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 427 646198 834756 540917 507205 025840 953957 144993 563338 804574 405096 559256 046169 195483 120316 932318 384466 840510 442412 678460 827822 958846 361924 895012 346181 724707 > 8¹⁶⁹ [i]