MinT - Best Known (49, 117, s)-Nets in Base 8

Best Known (49, 117, s)-Nets in Base 8

(49, 117, 98)-Net over F₈ — Constructive and digital

Digital (49, 117, 98)-net over F₈, using

t-expansion [i] based on digital (37, 117, 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]

(49, 117, 144)-Net over F₈ — Digital

Digital (49, 117, 144)-net over F₈, using

t-expansion [i] based on digital (45, 117, 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]

(49, 117, 2456)-Net in Base 8 — Upper bound on s

There is no (49, 117, 2457)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4617 494092 147840 787152 827301 727185 370413 158557 205527 162884 739627 529618 073945 794628 720427 399014 930520 561840 > 8¹¹⁷ [i]