MinT - Best Known (42, 126, s)-Nets in Base 5

Best Known (42, 126, s)-Nets in Base 5

(42, 126, 78)-Net over F₅ — Constructive and digital

Digital (42, 126, 78)-net over F₅, using

t-expansion [i] based on digital (38, 126, 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, 126, 80)-Net over F₅ — Digital

Digital (42, 126, 80)-net over F₅, using

t-expansion [i] based on digital (41, 126, 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, 126, 485)-Net in Base 5 — Upper bound on s

There is no (42, 126, 486)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12097 656527 781712 528959 795323 911574 510876 111259 804075 799136 917564 818907 659866 183865 191425 > 5¹²⁶ [i]