MinT - Best Known (152−97, 152, s)-Nets in Base 8

Best Known (152−97, 152, s)-Nets in Base 8

(152−97, 152, 98)-Net over F₈ — Constructive and digital

Digital (55, 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]

(152−97, 152, 144)-Net over F₈ — Digital

Digital (55, 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]

(152−97, 152, 1826)-Net in Base 8 — Upper bound on s

There is no (55, 152, 1827)-net in base 8, because

1 times m-reduction [i] would yield (55, 151, 1827)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23773 659668 179411 432534 728828 992457 179864 196271 493700 436497 252598 592907 260788 015630 512982 432605 768338 366898 712163 281734 977066 667748 831344 > 8¹⁵¹ [i]