MinT - Best Known (70, 70+80, s)-Nets in Base 5

Best Known (70, 70+80, s)-Nets in Base 5

(70, 70+80, 82)-Net over F₅ — Constructive and digital

Digital (70, 150, 82)-net over F₅, using

t-expansion [i] based on digital (48, 150, 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]

(70, 70+80, 132)-Net over F₅ — Digital

Digital (70, 150, 132)-net over F₅, using

t-expansion [i] based on digital (67, 150, 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]

(70, 70+80, 1618)-Net in Base 5 — Upper bound on s

There is no (70, 150, 1619)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 711 780237 092339 056371 048718 673825 901864 145392 902048 050625 172270 683129 575350 790409 009025 613493 951612 506209 > 5¹⁵⁰ [i]