MinT - Best Known (48, 48+110, s)-Nets in Base 8

Best Known (48, 48+110, s)-Nets in Base 8

(48, 48+110, 98)-Net over F₈ — Constructive and digital

Digital (48, 158, 98)-net over F₈, using

t-expansion [i] based on digital (37, 158, 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+110, 144)-Net over F₈ — Digital

Digital (48, 158, 144)-net over F₈, using

t-expansion [i] based on digital (45, 158, 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+110, 1163)-Net in Base 8 — Upper bound on s

There is no (48, 158, 1164)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 50450 931445 482190 332281 213916 629461 727150 121754 987965 644248 357713 399152 451196 823239 614543 634723 104700 803100 060636 890639 448590 559811 873296 849712 > 8¹⁵⁸ [i]