MinT - Best Known (63, 63+106, s)-Nets in Base 8

Best Known (63, 63+106, s)-Nets in Base 8

(63, 63+106, 98)-Net over F₈ — Constructive and digital

Digital (63, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(63, 63+106, 144)-Net over F₈ — Digital

Digital (63, 169, 144)-net over F₈, using

t-expansion [i] based on digital (45, 169, 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]

(63, 63+106, 2196)-Net in Base 8 — Upper bound on s

There is no (63, 169, 2197)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 420 489192 940239 799907 679957 604414 616150 647037 814442 305034 862119 728685 419381 804371 619376 054923 634596 674549 418488 222625 907455 731939 238817 398497 750390 766112 > 8¹⁶⁹ [i]