MinT - Best Known (58, 115, s)-Nets in Base 5

Best Known (58, 115, s)-Nets in Base 5

(58, 115, 82)-Net over F₅ — Constructive and digital

Digital (58, 115, 82)-net over F₅, using

t-expansion [i] based on digital (48, 115, 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]

(58, 115, 120)-Net over F₅ — Digital

Digital (58, 115, 120)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 115, 1959)-Net in Base 5 — Upper bound on s

There is no (58, 115, 1960)-net in base 5, because

1 times m-reduction [i] would yield (58, 114, 1960)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 169222 905075 377700 503461 375260 769551 182475 339434 534198 597866 007415 411837 889537 > 5¹¹⁴ [i]