MinT - Best Known (169−119, 169, s)-Nets in Base 8

Best Known (169−119, 169, s)-Nets in Base 8

(169−119, 169, 98)-Net over F₈ — Constructive and digital

Digital (50, 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]

(169−119, 169, 144)-Net over F₈ — Digital

Digital (50, 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]

(169−119, 169, 1178)-Net in Base 8 — Upper bound on s

There is no (50, 169, 1179)-net in base 8, because

1 times m-reduction [i] would yield (50, 168, 1179)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 903145 265095 369490 280088 557240 705476 081554 510759 822253 409407 508692 435411 116713 644940 995069 020031 925336 244899 879496 543204 313983 939961 321248 865280 502368 > 8¹⁶⁸ [i]