MinT - Best Known (49, 49+49, s)-Nets in Base 5

Best Known (49, 49+49, s)-Nets in Base 5

(49, 49+49, 82)-Net over F₅ — Constructive and digital

Digital (49, 98, 82)-net over F₅, using

t-expansion [i] based on digital (48, 98, 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]

(49, 49+49, 103)-Net over F₅ — Digital

Digital (49, 98, 103)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+49, 1620)-Net in Base 5 — Upper bound on s

There is no (49, 98, 1621)-net in base 5, because

1 times m-reduction [i] would yield (49, 97, 1621)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 63 536479 076778 189233 117323 389344 075484 237919 431965 245144 575986 584225 > 5⁹⁷ [i]