MinT - Best Known (170−122, 170, s)-Nets in Base 8

Best Known (170−122, 170, s)-Nets in Base 8

(170−122, 170, 98)-Net over F₈ — Constructive and digital

Digital (48, 170, 98)-net over F₈, using

t-expansion [i] based on digital (37, 170, 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]

(170−122, 170, 144)-Net over F₈ — Digital

Digital (48, 170, 144)-net over F₈, using

t-expansion [i] based on digital (45, 170, 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]

(170−122, 170, 1068)-Net in Base 8 — Upper bound on s

There is no (48, 170, 1069)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3514 870235 842431 935995 968553 686254 006064 870388 871473 583241 954581 989706 008271 892116 002415 658219 226018 104708 683771 340871 033992 604882 987344 015656 241152 047616 > 8¹⁷⁰ [i]