MinT - Best Known (49, 49+85, s)-Nets in Base 8

Best Known (49, 49+85, s)-Nets in Base 8

(49, 49+85, 98)-Net over F₈ — Constructive and digital

Digital (49, 134, 98)-net over F₈, using

t-expansion [i] based on digital (37, 134, 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]

(49, 49+85, 144)-Net over F₈ — Digital

Digital (49, 134, 144)-net over F₈, using

t-expansion [i] based on digital (45, 134, 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]

(49, 49+85, 1681)-Net in Base 8 — Upper bound on s

There is no (49, 134, 1682)-net in base 8, because

1 times m-reduction [i] would yield (49, 133, 1682)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 302986 317698 342198 402509 762839 771964 883235 205851 598230 028340 371238 910866 840705 681575 322334 163965 428483 892536 498408 044192 > 8¹³³ [i]