MinT - Best Known (65, 160, s)-Nets in Base 8

Best Known (65, 160, s)-Nets in Base 8

(65, 160, 98)-Net over F₈ — Constructive and digital

Digital (65, 160, 98)-net over F₈, using

t-expansion [i] based on digital (37, 160, 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]

(65, 160, 144)-Net over F₈ — Digital

Digital (65, 160, 144)-net over F₈, using

t-expansion [i] based on digital (45, 160, 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]

(65, 160, 2949)-Net in Base 8 — Upper bound on s

There is no (65, 160, 2950)-net in base 8, because

1 times m-reduction [i] would yield (65, 159, 2950)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 391320 808145 378660 665612 706558 052236 131474 906550 476095 834051 964266 860949 002862 696661 894250 094752 931252 576943 497835 088824 881719 823490 491292 736832 > 8¹⁵⁹ [i]