MinT - Best Known (65, 161, s)-Nets in Base 8

Best Known (65, 161, s)-Nets in Base 8

(65, 161, 98)-Net over F₈ — Constructive and digital

Digital (65, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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, 161, 144)-Net over F₈ — Digital

Digital (65, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 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, 161, 2832)-Net in Base 8 — Upper bound on s

There is no (65, 161, 2833)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 125403 069456 246360 184814 525791 451353 308890 860910 537935 881714 641138 012863 862486 162278 802504 200964 361135 848109 036370 023565 381377 029042 899604 435928 > 8¹⁶¹ [i]