MinT - Best Known (61, 61+92, s)-Nets in Base 8

Best Known (61, 61+92, s)-Nets in Base 8

(61, 61+92, 98)-Net over F₈ — Constructive and digital

Digital (61, 153, 98)-net over F₈, using

t-expansion [i] based on digital (37, 153, 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+92, 144)-Net over F₈ — Digital

Digital (61, 153, 144)-net over F₈, using

t-expansion [i] based on digital (45, 153, 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+92, 2564)-Net in Base 8 — Upper bound on s

There is no (61, 153, 2565)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 500891 243253 765501 312120 719906 197435 230801 583600 974546 172136 945167 969537 925808 615231 188774 735933 524381 030534 368634 725685 620321 642801 475328 > 8¹⁵³ [i]