MinT - Best Known (45, 45+103, s)-Nets in Base 8

Best Known (45, 45+103, s)-Nets in Base 8

(45, 45+103, 98)-Net over F₈ — Constructive and digital

Digital (45, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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]

(45, 45+103, 144)-Net over F₈ — Digital

Digital (45, 148, 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]

(45, 45+103, 1105)-Net in Base 8 — Upper bound on s

There is no (45, 148, 1106)-net in base 8, because

1 times m-reduction [i] would yield (45, 147, 1106)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 926828 393334 053561 886585 791459 217073 181969 143001 537815 288608 439120 712562 952751 158808 543004 414715 836748 401539 372826 429032 154789 073888 > 8¹⁴⁷ [i]