MinT - Best Known (147−85, 147, s)-Nets in Base 8

Best Known (147−85, 147, s)-Nets in Base 8

(147−85, 147, 98)-Net over F₈ — Constructive and digital

Digital (62, 147, 98)-net over F₈, using

t-expansion [i] based on digital (37, 147, 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]

(147−85, 147, 144)-Net over F₈ — Digital

Digital (62, 147, 144)-net over F₈, using

t-expansion [i] based on digital (45, 147, 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]

(147−85, 147, 3224)-Net in Base 8 — Upper bound on s

There is no (62, 147, 3225)-net in base 8, because

1 times m-reduction [i] would yield (62, 146, 3225)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 713820 978536 319760 599065 603557 814723 070808 507810 252210 522411 620450 720061 311521 572273 944372 938078 434898 643892 141681 389789 354795 230304 > 8¹⁴⁶ [i]