MinT - Best Known (67−59, 67, s)-Nets in Base 32

Best Known (67−59, 67, s)-Nets in Base 32

(67−59, 67, 98)-Net over F₃₂ — Constructive and digital

Digital (8, 67, 98)-net over F₃₂, using

t-expansion [i] based on digital (7, 67, 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]

(67−59, 67, 988)-Net in Base 32 — Upper bound on s

There is no (8, 67, 989)-net in base 32, because

1 times m-reduction [i] would yield (8, 66, 989)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2248 090978 138464 211244 539645 817824 613069 910527 621665 003663 411011 203030 559014 861812 228504 440123 556192 > 32⁶⁶ [i]