MinT - Best Known (49, 49+114, s)-Nets in Base 8

Best Known (49, 49+114, s)-Nets in Base 8

(49, 49+114, 98)-Net over F₈ — Constructive and digital

Digital (49, 163, 98)-net over F₈, using

t-expansion [i] based on digital (37, 163, 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+114, 144)-Net over F₈ — Digital

Digital (49, 163, 144)-net over F₈, using

t-expansion [i] based on digital (45, 163, 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+114, 1170)-Net in Base 8 — Upper bound on s

There is no (49, 163, 1171)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1646 056407 323681 052268 173352 472272 692990 542916 941158 781030 369252 603998 602860 873044 599680 171497 486412 919515 294202 670339 854800 114348 285316 976279 816864 > 8¹⁶³ [i]