MinT - Best Known (142−70, 142, s)-Nets in Base 5

Best Known (142−70, 142, s)-Nets in Base 5

(142−70, 142, 93)-Net over F₅ — Constructive and digital

Digital (72, 142, 93)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (6, 41, 21)-net over F₅, using
  - net from sequence [i] based on digital (6, 20)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 6 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 101, 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]

(142−70, 142, 146)-Net over F₅ — Digital

Digital (72, 142, 146)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−70, 142, 2356)-Net in Base 5 — Upper bound on s

There is no (72, 142, 2357)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1798 799712 351494 516814 340156 356545 965279 234433 999209 242955 847305 585423 236005 164025 304896 117599 832845 > 5¹⁴² [i]