MinT - Best Known (125−78, 125, s)-Nets in Base 8

Best Known (125−78, 125, s)-Nets in Base 8

(125−78, 125, 98)-Net over F₈ — Constructive and digital

Digital (47, 125, 98)-net over F₈, using

t-expansion [i] based on digital (37, 125, 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]

(125−78, 125, 144)-Net over F₈ — Digital

Digital (47, 125, 144)-net over F₈, using

t-expansion [i] based on digital (45, 125, 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]

(125−78, 125, 1700)-Net in Base 8 — Upper bound on s

There is no (47, 125, 1701)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 77371 481558 874066 755946 999297 620082 823237 062484 136208 781635 486622 931464 559411 687499 558051 316461 208136 693486 352256 > 8¹²⁵ [i]