MinT - Best Known (9, 9+53, s)-Nets in Base 8

Best Known (9, 9+53, s)-Nets in Base 8

(9, 9+53, 45)-Net over F₈ — Constructive and digital

Digital (9, 62, 45)-net over F₈, using

net from sequence [i] based on digital (9, 44)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]

(9, 9+53, 123)-Net in Base 8 — Upper bound on s

There is no (9, 62, 124)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶², 124, S₈, 53), but
- the linear programming bound shows that MÂ â‰¥ 5 692949 743809 823748 752715 007842 107611 249295 028243 344797 951714 898849 104111 844393 823936 843119 205282 071569 708702 807226 270016 713860 371441 516544 / 55066 325463 939448 183906 032918 579181 533277 571772 774951 609871 815924 807464 133417 564889 > 8⁶² [i]