MinT - Best Known (47, 47+63, s)-Nets in Base 8

Best Known (47, 47+63, s)-Nets in Base 8

(47, 47+63, 98)-Net over F₈ — Constructive and digital

Digital (47, 110, 98)-net over F₈, using

t-expansion [i] based on digital (37, 110, 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, 47+63, 144)-Net over F₈ — Digital

Digital (47, 110, 144)-net over F₈, using

t-expansion [i] based on digital (45, 110, 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, 47+63, 2637)-Net in Base 8 — Upper bound on s

There is no (47, 110, 2638)-net in base 8, because

1 times m-reduction [i] would yield (47, 109, 2638)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 276 125648 199142 005409 224454 828162 261638 610810 224473 390919 639492 138469 129598 613152 162833 713969 822432 > 8¹⁰⁹ [i]