MinT - Best Known (152−101, 152, s)-Nets in Base 8

Best Known (152−101, 152, s)-Nets in Base 8

(152−101, 152, 98)-Net over F₈ — Constructive and digital

Digital (51, 152, 98)-net over F₈, using

t-expansion [i] based on digital (37, 152, 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]

(152−101, 152, 144)-Net over F₈ — Digital

Digital (51, 152, 144)-net over F₈, using

t-expansion [i] based on digital (45, 152, 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]

(152−101, 152, 1454)-Net in Base 8 — Upper bound on s

There is no (51, 152, 1455)-net in base 8, because

1 times m-reduction [i] would yield (51, 151, 1455)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23944 046620 077557 876385 084896 575931 301391 310421 127500 241060 031143 029216 535122 381653 688194 986230 297539 738249 814576 448250 961445 877634 024312 > 8¹⁵¹ [i]