MinT - Best Known (48, 48+100, s)-Nets in Base 8

Best Known (48, 48+100, s)-Nets in Base 8

(48, 48+100, 98)-Net over F₈ — Constructive and digital

Digital (48, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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+100, 144)-Net over F₈ — Digital

Digital (48, 148, 144)-net over F₈, using

t-expansion [i] based on digital (45, 148, 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+100, 1279)-Net in Base 8 — Upper bound on s

There is no (48, 148, 1280)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 583345 620607 663428 675457 570596 783835 160238 370878 351032 467663 463904 163070 586051 914572 282558 795845 666908 068626 574468 831649 588966 174201 > 8¹⁴⁸ [i]