MinT - Best Known (61, 61+90, s)-Nets in Base 8

Best Known (61, 61+90, s)-Nets in Base 8

(61, 61+90, 98)-Net over F₈ — Constructive and digital

Digital (61, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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]

(61, 61+90, 144)-Net over F₈ — Digital

Digital (61, 151, 144)-net over F₈, using

t-expansion [i] based on digital (45, 151, 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]

(61, 61+90, 2672)-Net in Base 8 — Upper bound on s

There is no (61, 151, 2673)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23585 828346 351033 545455 827777 240143 741645 905629 193309 305899 839114 777280 069857 571236 572335 060615 287558 824510 594498 525095 478694 695678 896560 > 8¹⁵¹ [i]