MinT - Best Known (65, 65+82, s)-Nets in Base 5

Best Known (65, 65+82, s)-Nets in Base 5

(65, 65+82, 82)-Net over F₅ — Constructive and digital

Digital (65, 147, 82)-net over F₅, using

t-expansion [i] based on digital (48, 147, 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]

(65, 65+82, 120)-Net over F₅ — Digital

Digital (65, 147, 120)-net over F₅, using

t-expansion [i] based on digital (61, 147, 120)-net over F₅, using
- net from sequence [i] based on digital (61, 119)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(65, 65+82, 1263)-Net in Base 5 — Upper bound on s

There is no (65, 147, 1264)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 614964 317836 977198 014351 603496 462648 668445 644596 219471 422565 922104 797981 522997 258932 333483 702508 914625 > 5¹⁴⁷ [i]