MinT - Best Known (150−74, 150, s)-Nets in Base 5

Best Known (150−74, 150, s)-Nets in Base 5

(150−74, 150, 95)-Net over F₅ — Constructive and digital

Digital (76, 150, 95)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (8, 45, 23)-net over F₅, using
  - net from sequence [i] based on digital (8, 22)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 7, N(F)Â =Â 22, and 1 place with degree 2 [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using an explicitly constructive algebraic function field [i]
2. digital (31, 105, 72)-net over F₅, using
  - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
      - an explicitly constructive algebraic function field [i]

(150−74, 150, 152)-Net over F₅ — Digital

Digital (76, 150, 152)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−74, 150, 2470)-Net in Base 5 — Upper bound on s

There is no (76, 150, 2471)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 706 857770 109270 464966 546669 791109 081355 813199 338560 757303 123231 911542 195847 739733 499172 016714 702555 415565 > 5¹⁵⁰ [i]