MinT - Best Known (49, 49+71, s)-Nets in Base 8

Best Known (49, 49+71, s)-Nets in Base 8

(49, 49+71, 98)-Net over F₈ — Constructive and digital

Digital (49, 120, 98)-net over F₈, using

t-expansion [i] based on digital (37, 120, 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+71, 144)-Net over F₈ — Digital

Digital (49, 120, 144)-net over F₈, using

t-expansion [i] based on digital (45, 120, 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+71, 2315)-Net in Base 8 — Upper bound on s

There is no (49, 120, 2316)-net in base 8, because

1 times m-reduction [i] would yield (49, 119, 2316)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 297403 548092 869885 722872 449592 142837 935621 622580 572040 270850 761420 495374 342367 338671 868012 330398 076424 067784 > 8¹¹⁹ [i]