MinT - Best Known (47, 47+117, s)-Nets in Base 8

Best Known (47, 47+117, s)-Nets in Base 8

(47, 47+117, 98)-Net over F₈ — Constructive and digital

Digital (47, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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+117, 144)-Net over F₈ — Digital

Digital (47, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 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+117, 1070)-Net in Base 8 — Upper bound on s

There is no (47, 164, 1071)-net in base 8, because

1 times m-reduction [i] would yield (47, 163, 1071)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1639 251750 260708 244921 552998 594617 344041 862030 941867 233901 742612 073119 584841 673154 664953 560892 416446 168482 547905 897238 234658 456500 523407 008509 868224 > 8¹⁶³ [i]