MinT - Best Known (104−56, 104, s)-Nets in Base 8

Best Known (104−56, 104, s)-Nets in Base 8

(104−56, 104, 98)-Net over F₈ — Constructive and digital

Digital (48, 104, 98)-net over F₈, using

t-expansion [i] based on digital (37, 104, 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]

(104−56, 104, 144)-Net over F₈ — Digital

Digital (48, 104, 144)-net over F₈, using

t-expansion [i] based on digital (45, 104, 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]

(104−56, 104, 3632)-Net in Base 8 — Upper bound on s

There is no (48, 104, 3633)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8402 030632 355153 179366 926092 286188 996726 525631 074302 179805 170296 938278 217036 014582 313173 122728 > 8¹⁰⁴ [i]