MinT - Best Known (48, 48+72, s)-Nets in Base 8

Best Known (48, 48+72, s)-Nets in Base 8

(48, 48+72, 98)-Net over F₈ — Constructive and digital

Digital (48, 120, 98)-net over F₈, using

t-expansion [i] based on digital (37, 120, 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]

(48, 48+72, 144)-Net over F₈ — Digital

Digital (48, 120, 144)-net over F₈, using

t-expansion [i] based on digital (45, 120, 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]

(48, 48+72, 2066)-Net in Base 8 — Upper bound on s

There is no (48, 120, 2067)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 371536 058099 125991 628812 468963 367095 996395 879919 450705 616064 606338 104440 620171 941317 454048 550469 425674 786560 > 8¹²⁰ [i]