MinT - Best Known (58, 58+109, s)-Nets in Base 8

Best Known (58, 58+109, s)-Nets in Base 8

(58, 58+109, 98)-Net over F₈ — Constructive and digital

Digital (58, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(58, 58+109, 144)-Net over F₈ — Digital

Digital (58, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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]

(58, 58+109, 1754)-Net in Base 8 — Upper bound on s

There is no (58, 167, 1755)-net in base 8, because

1 times m-reduction [i] would yield (58, 166, 1755)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818771 355418 724412 489055 815936 375597 300049 412437 905498 986408 816770 960299 690483 109176 868425 477980 538069 855092 057626 167990 646459 922110 609802 273901 863684 > 8¹⁶⁶ [i]