MinT - Best Known (138−80, 138, s)-Nets in Base 8

Best Known (138−80, 138, s)-Nets in Base 8

(138−80, 138, 98)-Net over F₈ — Constructive and digital

Digital (58, 138, 98)-net over F₈, using

t-expansion [i] based on digital (37, 138, 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]

(138−80, 138, 144)-Net over F₈ — Digital

Digital (58, 138, 144)-net over F₈, using

t-expansion [i] based on digital (45, 138, 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]

(138−80, 138, 2914)-Net in Base 8 — Upper bound on s

There is no (58, 138, 2915)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42368 928020 195433 898687 746650 342028 817843 434831 324194 855557 492395 123657 295223 666006 269365 573817 124178 062097 812516 571511 923240 > 8¹³⁸ [i]