MinT - Best Known (8, 68, s)-Nets in Base 32

Best Known (8, 68, s)-Nets in Base 32

(8, 68, 98)-Net over F₃₂ — Constructive and digital

Digital (8, 68, 98)-net over F₃₂, using

t-expansion [i] based on digital (7, 68, 98)-net over F₃₂, using
- net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
    - a function field by SÃ©mirat [i]

(8, 68, 987)-Net in Base 32 — Upper bound on s

There is no (8, 68, 988)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 299444 360761 380317 503792 176057 002361 292634 528664 989237 837117 461257 416840 712941 771996 170020 945742 733424 > 32⁶⁸ [i]