MinT - Best Known (47, 105, s)-Nets in Base 8

Best Known (47, 105, s)-Nets in Base 8

(47, 105, 98)-Net over F₈ — Constructive and digital

Digital (47, 105, 98)-net over F₈, using

t-expansion [i] based on digital (37, 105, 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, 105, 144)-Net over F₈ — Digital

Digital (47, 105, 144)-net over F₈, using

t-expansion [i] based on digital (45, 105, 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, 105, 3085)-Net in Base 8 — Upper bound on s

There is no (47, 105, 3086)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 67217 378246 033229 650576 022885 402968 922196 388100 935626 511509 215850 139381 683577 437657 334517 204544 > 8¹⁰⁵ [i]