MinT - Best Known (68, 146, s)-Nets in Base 5

Best Known (68, 146, s)-Nets in Base 5

(68, 146, 82)-Net over F₅ — Constructive and digital

Digital (68, 146, 82)-net over F₅, using

t-expansion [i] based on digital (48, 146, 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]

(68, 146, 132)-Net over F₅ — Digital

Digital (68, 146, 132)-net over F₅, using

t-expansion [i] based on digital (67, 146, 132)-net over F₅, using
- net from sequence [i] based on digital (67, 131)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 67 and N(F) ≥ 132, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(68, 146, 1563)-Net in Base 5 — Upper bound on s

There is no (68, 146, 1564)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 128651 737358 600768 894451 682426 469516 726063 337578 816012 337414 244936 274564 660472 306234 757360 197901 358065 > 5¹⁴⁶ [i]