MinT - Best Known (169−107, 169, s)-Nets in Base 8

Best Known (169−107, 169, s)-Nets in Base 8

(169−107, 169, 98)-Net over F₈ — Constructive and digital

Digital (62, 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]

(169−107, 169, 144)-Net over F₈ — Digital

Digital (62, 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]

(169−107, 169, 2111)-Net in Base 8 — Upper bound on s

There is no (62, 169, 2112)-net in base 8, because

1 times m-reduction [i] would yield (62, 168, 2112)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 622968 677132 663991 585563 736641 486845 024441 673169 182161 242911 989922 803333 233255 852947 520836 673766 672017 577947 276608 420182 492518 580938 687209 250439 743671 > 8¹⁶⁸ [i]