MinT - Best Known (48, 48+69, s)-Nets in Base 8

Best Known (48, 48+69, s)-Nets in Base 8

(48, 48+69, 98)-Net over F₈ — Constructive and digital

Digital (48, 117, 98)-net over F₈, using

t-expansion [i] based on digital (37, 117, 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]

(48, 48+69, 144)-Net over F₈ — Digital

Digital (48, 117, 144)-net over F₈, using

t-expansion [i] based on digital (45, 117, 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]

(48, 48+69, 2309)-Net in Base 8 — Upper bound on s

There is no (48, 117, 2310)-net in base 8, because

1 times m-reduction [i] would yield (48, 116, 2310)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 577 417729 286792 326074 545850 982841 439885 813501 233601 061141 622806 010346 657158 897748 562034 398382 979042 106800 > 8¹¹⁶ [i]