MinT - Best Known (62, 156, s)-Nets in Base 8

Best Known (62, 156, s)-Nets in Base 8

(62, 156, 98)-Net over F₈ — Constructive and digital

Digital (62, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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]

(62, 156, 144)-Net over F₈ — Digital

Digital (62, 156, 144)-net over F₈, using

t-expansion [i] based on digital (45, 156, 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]

(62, 156, 2579)-Net in Base 8 — Upper bound on s

There is no (62, 156, 2580)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 769 145898 012008 148046 771339 447287 444839 076837 696755 223068 078883 039569 043438 244706 193864 751967 539325 103228 455815 121379 640901 865165 747215 534144 > 8¹⁵⁶ [i]