MinT - Best Known (64, 169, s)-Nets in Base 8

Best Known (64, 169, s)-Nets in Base 8

(64, 169, 98)-Net over F₈ — Constructive and digital

Digital (64, 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]

(64, 169, 144)-Net over F₈ — Digital

Digital (64, 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]

(64, 169, 2357)-Net in Base 8 — Upper bound on s

There is no (64, 169, 2358)-net in base 8, because

1 times m-reduction [i] would yield (64, 168, 2358)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 798340 194864 184486 942950 835559 599088 596018 432537 338110 805397 965285 707518 979350 422720 716383 491918 172518 159012 196753 970842 753535 451693 339320 012871 748957 > 8¹⁶⁸ [i]