MinT - Best Known (49, 49+63, s)-Nets in Base 8

Best Known (49, 49+63, s)-Nets in Base 8

(49, 49+63, 98)-Net over F₈ — Constructive and digital

Digital (49, 112, 98)-net over F₈, using

t-expansion [i] based on digital (37, 112, 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+63, 144)-Net over F₈ — Digital

Digital (49, 112, 144)-net over F₈, using

t-expansion [i] based on digital (45, 112, 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+63, 3018)-Net in Base 8 — Upper bound on s

There is no (49, 112, 3019)-net in base 8, because

1 times m-reduction [i] would yield (49, 111, 3019)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17577 975023 918808 263426 938280 978496 696554 116996 489586 842692 817215 909196 149095 592366 472025 584646 144448 > 8¹¹¹ [i]