MinT - Best Known (67, 67+72, s)-Nets in Base 5

Best Known (67, 67+72, s)-Nets in Base 5

(67, 67+72, 82)-Net over F₅ — Constructive and digital

Digital (67, 139, 82)-net over F₅, using

t-expansion [i] based on digital (48, 139, 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]

(67, 67+72, 132)-Net over F₅ — Digital

Digital (67, 139, 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]

(67, 67+72, 1757)-Net in Base 5 — Upper bound on s

There is no (67, 139, 1758)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 354823 246778 864079 242623 206916 793718 453815 646260 969692 659553 690667 600672 959699 550970 970265 321025 > 5¹³⁹ [i]