MinT - Best Known (106−56, 106, s)-Nets in Base 5

Best Known (106−56, 106, s)-Nets in Base 5

(106−56, 106, 82)-Net over F₅ — Constructive and digital

Digital (50, 106, 82)-net over F₅, using

t-expansion [i] based on digital (48, 106, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(106−56, 106, 96)-Net over F₅ — Digital

Digital (50, 106, 96)-net over F₅, using

t-expansion [i] based on digital (49, 106, 96)-net over F₅, using
- net from sequence [i] based on digital (49, 95)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 49 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(106−56, 106, 1230)-Net in Base 5 — Upper bound on s

There is no (50, 106, 1231)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 126 020632 956096 383804 597173 540692 670681 847639 846037 011314 903718 789640 664465 > 5¹⁰⁶ [i]