MinT - Best Known (48, 48+98, s)-Nets in Base 8

Best Known (48, 48+98, s)-Nets in Base 8

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

Digital (48, 146, 98)-net over F₈, using

t-expansion [i] based on digital (37, 146, 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+98, 144)-Net over F₈ — Digital

Digital (48, 146, 144)-net over F₈, using

t-expansion [i] based on digital (45, 146, 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+98, 1309)-Net in Base 8 — Upper bound on s

There is no (48, 146, 1310)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 734998 351268 548442 700020 085098 060391 548661 191458 981639 360560 321703 463104 515133 403149 011378 743488 432844 593420 614804 782091 041984 602824 > 8¹⁴⁶ [i]