MinT - Best Known (42, 42+100, s)-Nets in Base 5

Best Known (42, 42+100, s)-Nets in Base 5

(42, 42+100, 78)-Net over F₅ — Constructive and digital

Digital (42, 142, 78)-net over F₅, using

t-expansion [i] based on digital (38, 142, 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]

(42, 42+100, 80)-Net over F₅ — Digital

Digital (42, 142, 80)-net over F₅, using

t-expansion [i] based on digital (41, 142, 80)-net over F₅, using
- net from sequence [i] based on digital (41, 79)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 41 and N(F) ≥ 80, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(42, 42+100, 434)-Net in Base 5 — Upper bound on s

There is no (42, 142, 435)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1867 198088 071203 212563 662923 540555 591148 061394 024805 449008 766109 717956 996280 611468 300616 904264 136121 > 5¹⁴² [i]