MinT - Best Known (167−122, 167, s)-Nets in Base 8

Best Known (167−122, 167, s)-Nets in Base 8

(167−122, 167, 98)-Net over F₈ — Constructive and digital

Digital (45, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(167−122, 167, 144)-Net over F₈ — Digital

Digital (45, 167, 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]

(167−122, 167, 960)-Net in Base 8 — Upper bound on s

There is no (45, 167, 961)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 699817 713862 218072 069425 046047 732107 238340 422835 262679 007193 237296 731212 233108 633366 046862 003164 987492 654158 118331 719151 810718 487131 908309 143092 556352 > 8¹⁶⁷ [i]