MinT - Best Known (58, 58+82, s)-Nets in Base 5

Best Known (58, 58+82, s)-Nets in Base 5

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

Digital (58, 140, 82)-net over F₅, using

t-expansion [i] based on digital (48, 140, 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, 58+82, 112)-Net over F₅ — Digital

Digital (58, 140, 112)-net over F₅, using

t-expansion [i] based on digital (57, 140, 112)-net over F₅, using
- net from sequence [i] based on digital (57, 111)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 57 and N(F) ≥ 112, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(58, 58+82, 953)-Net in Base 5 — Upper bound on s

There is no (58, 140, 954)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 74 377960 374527 085835 710700 166385 238818 264585 930885 991935 997897 856284 775513 273480 290433 630636 589545 > 5¹⁴⁰ [i]