MinT - Best Known (168−122, 168, s)-Nets in Base 8

Best Known (168−122, 168, s)-Nets in Base 8

(168−122, 168, 98)-Net over F₈ — Constructive and digital

Digital (46, 168, 98)-net over F₈, using

t-expansion [i] based on digital (37, 168, 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]

(168−122, 168, 144)-Net over F₈ — Digital

Digital (46, 168, 144)-net over F₈, using

t-expansion [i] based on digital (45, 168, 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]

(168−122, 168, 995)-Net in Base 8 — Upper bound on s

There is no (46, 168, 996)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 54 759886 362080 259520 988323 318929 955347 390511 380158 986178 049069 880367 350363 715476 620429 965601 126656 420001 975286 455871 184072 955359 963532 530582 543517 798608 > 8¹⁶⁸ [i]