MinT - Best Known (38, 38+68, s)-Nets in Base 5

Best Known (38, 38+68, s)-Nets in Base 5

(38, 38+68, 78)-Net over F₅ — Constructive and digital

Digital (38, 106, 78)-net over F₅, using

net from sequence [i] based on digital (38, 77)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
  - an explicitly constructive algebraic function field [i]

(38, 38+68, 486)-Net in Base 5 — Upper bound on s

There is no (38, 106, 487)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 126 691728 862483 970215 833290 092650 259686 350412 240397 035559 799093 077391 341945 > 5¹⁰⁶ [i]