MinT - Best Known (64, 171, s)-Nets in Base 8

Best Known (64, 171, s)-Nets in Base 8

(64, 171, 98)-Net over F₈ — Constructive and digital

Digital (64, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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, 171, 144)-Net over F₈ — Digital

Digital (64, 171, 144)-net over F₈, using

t-expansion [i] based on digital (45, 171, 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, 171, 2286)-Net in Base 8 — Upper bound on s

There is no (64, 171, 2287)-net in base 8, because

1 times m-reduction [i] would yield (64, 170, 2287)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3422 557749 473391 086982 674727 166691 386042 459387 824684 006526 822001 689176 530053 731312 057476 596660 474064 364949 864010 838365 934373 535087 070975 303899 471136 881096 > 8¹⁷⁰ [i]