MinT - Best Known (48, 48+43, s)-Nets in Base 5

Best Known (48, 48+43, s)-Nets in Base 5

(48, 48+43, 82)-Net over F₅ — Constructive and digital

Digital (48, 91, 82)-net over F₅, using

net from sequence [i] based on digital (48, 81)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
  - an explicitly constructive algebraic function field [i]

(48, 48+43, 117)-Net over F₅ — Digital

Digital (48, 91, 117)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+43, 2132)-Net in Base 5 — Upper bound on s

There is no (48, 91, 2133)-net in base 5, because

1 times m-reduction [i] would yield (48, 90, 2133)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 810 087221 958530 538930 712626 526908 401895 005641 033979 164082 496325 > 5⁹⁰ [i]