MinT - Best Known (49, 49+111, s)-Nets in Base 8

Best Known (49, 49+111, s)-Nets in Base 8

(49, 49+111, 98)-Net over F₈ — Constructive and digital

Digital (49, 160, 98)-net over F₈, using

t-expansion [i] based on digital (37, 160, 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, 49+111, 144)-Net over F₈ — Digital

Digital (49, 160, 144)-net over F₈, using

t-expansion [i] based on digital (45, 160, 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, 49+111, 1209)-Net in Base 8 — Upper bound on s

There is no (49, 160, 1210)-net in base 8, because

1 times m-reduction [i] would yield (49, 159, 1210)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 400562 439617 847425 197695 300011 043768 363203 304573 529026 458921 747656 548881 780907 264178 186138 265694 251356 409906 429910 481258 390685 780448 124717 100180 > 8¹⁵⁹ [i]