MinT - Best Known (47, 156, s)-Nets in Base 8

Best Known (47, 156, s)-Nets in Base 8

(47, 156, 98)-Net over F₈ — Constructive and digital

Digital (47, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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]

(47, 156, 144)-Net over F₈ — Digital

Digital (47, 156, 144)-net over F₈, using

t-expansion [i] based on digital (45, 156, 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]

(47, 156, 1137)-Net in Base 8 — Upper bound on s

There is no (47, 156, 1138)-net in base 8, because

1 times m-reduction [i] would yield (47, 155, 1138)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 98 257528 076715 423312 367951 590523 338927 828849 928997 395060 614540 547736 795231 968416 551582 309853 377059 200608 820298 672708 183216 731000 702648 018976 > 8¹⁵⁵ [i]