MinT - Best Known (47, 47+75, s)-Nets in Base 8

Best Known (47, 47+75, s)-Nets in Base 8

(47, 47+75, 98)-Net over F₈ — Constructive and digital

Digital (47, 122, 98)-net over F₈, using

t-expansion [i] based on digital (37, 122, 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+75, 144)-Net over F₈ — Digital

Digital (47, 122, 144)-net over F₈, using

t-expansion [i] based on digital (45, 122, 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+75, 1856)-Net in Base 8 — Upper bound on s

There is no (47, 122, 1857)-net in base 8, because

1 times m-reduction [i] would yield (47, 121, 1857)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 854868 223549 386439 926371 710776 028130 783152 635216 233009 813837 172798 334122 575270 726927 743264 388979 373157 181376 > 8¹²¹ [i]