MinT - Best Known (70, 70+76, s)-Nets in Base 5

Best Known (70, 70+76, s)-Nets in Base 5

(70, 70+76, 82)-Net over F₅ — Constructive and digital

Digital (70, 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]

(70, 70+76, 132)-Net over F₅ — Digital

Digital (70, 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]

(70, 70+76, 1792)-Net in Base 5 — Upper bound on s

There is no (70, 146, 1793)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 122419 129770 754719 720098 235789 717871 398702 836200 262837 304728 744475 029591 581758 138133 939938 339210 651785 > 5¹⁴⁶ [i]