MinT - Best Known (153−106, 153, s)-Nets in Base 8

Best Known (153−106, 153, s)-Nets in Base 8

(153−106, 153, 98)-Net over F₈ — Constructive and digital

Digital (47, 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]

(153−106, 153, 144)-Net over F₈ — Digital

Digital (47, 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]

(153−106, 153, 1157)-Net in Base 8 — Upper bound on s

There is no (47, 153, 1158)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 542252 601161 142999 905097 570503 406614 374244 096732 421938 837554 889385 102889 939709 573325 186252 474734 985685 449558 095148 842969 819556 763238 522136 > 8¹⁵³ [i]