MinT - Best Known (73, 73+68, s)-Nets in Base 5

Best Known (73, 73+68, s)-Nets in Base 5

(73, 73+68, 95)-Net over F₅ — Constructive and digital

Digital (73, 141, 95)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (8, 42, 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, 99, 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]

(73, 73+68, 156)-Net over F₅ — Digital

Digital (73, 141, 156)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+68, 2654)-Net in Base 5 — Upper bound on s

There is no (73, 141, 2655)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 359 750042 603003 051366 272212 718076 256909 466952 874088 295362 100919 518966 893460 715607 049941 263306 588025 > 5¹⁴¹ [i]