MinT - Best Known (49, 49+51, s)-Nets in Base 5

Best Known (49, 49+51, s)-Nets in Base 5

(49, 49+51, 82)-Net over F₅ — Constructive and digital

Digital (49, 100, 82)-net over F₅, using

t-expansion [i] based on digital (48, 100, 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+51, 97)-Net over F₅ — Digital

Digital (49, 100, 97)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+51, 1472)-Net in Base 5 — Upper bound on s

There is no (49, 100, 1473)-net in base 5, because

1 times m-reduction [i] would yield (49, 99, 1473)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1581 372972 507942 718999 976529 003948 962920 899597 642735 663970 355520 756517 > 5⁹⁹ [i]