MinT - Best Known (139−90, 139, s)-Nets in Base 8

Best Known (139−90, 139, s)-Nets in Base 8

(139−90, 139, 98)-Net over F₈ — Constructive and digital

Digital (49, 139, 98)-net over F₈, using

t-expansion [i] based on digital (37, 139, 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]

(139−90, 139, 144)-Net over F₈ — Digital

Digital (49, 139, 144)-net over F₈, using

t-expansion [i] based on digital (45, 139, 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]

(139−90, 139, 1522)-Net in Base 8 — Upper bound on s

There is no (49, 139, 1523)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 340838 130313 995023 225865 614751 894061 856848 430773 201317 205344 115315 849091 581360 177665 140880 901472 207155 319979 454665 634754 664968 > 8¹³⁹ [i]