MinT - Best Known (154−101, 154, s)-Nets in Base 8

Best Known (154−101, 154, s)-Nets in Base 8

(154−101, 154, 98)-Net over F₈ — Constructive and digital

Digital (53, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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]

(154−101, 154, 144)-Net over F₈ — Digital

Digital (53, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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]

(154−101, 154, 1582)-Net in Base 8 — Upper bound on s

There is no (53, 154, 1583)-net in base 8, because

1 times m-reduction [i] would yield (53, 153, 1583)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 489835 195942 298079 412994 779901 358609 563282 847457 418181 482402 336768 076826 403873 120086 350849 288595 438966 016152 080113 753273 632784 727408 294752 > 8¹⁵³ [i]