MinT - Best Known (47, 172, s)-Nets in Base 8

Best Known (47, 172, s)-Nets in Base 8

(47, 172, 98)-Net over F₈ — Constructive and digital

Digital (47, 172, 98)-net over F₈, using

t-expansion [i] based on digital (37, 172, 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, 172, 144)-Net over F₈ — Digital

Digital (47, 172, 144)-net over F₈, using

t-expansion [i] based on digital (45, 172, 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, 172, 1019)-Net in Base 8 — Upper bound on s

There is no (47, 172, 1020)-net in base 8, because

1 times m-reduction [i] would yield (47, 171, 1020)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 27525 078196 268973 281823 996823 979053 708547 459843 767986 260768 091481 543838 254733 232139 628465 310490 416926 841011 811735 903173 283686 179970 483909 310514 799248 317008 > 8¹⁷¹ [i]