MinT - Best Known (106−80, 106, s)-Nets in Base 5

Best Known (106−80, 106, s)-Nets in Base 5

(106−80, 106, 51)-Net over F₅ — Constructive and digital

Digital (26, 106, 51)-net over F₅, using

t-expansion [i] based on digital (22, 106, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(106−80, 106, 55)-Net over F₅ — Digital

Digital (26, 106, 55)-net over F₅, using

t-expansion [i] based on digital (23, 106, 55)-net over F₅, using
- net from sequence [i] based on digital (23, 54)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(106−80, 106, 252)-Net in Base 5 — Upper bound on s

There is no (26, 106, 253)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 229824 386562 168188 858801 006846 210567 069623 445359 628054 662705 051876 797025 > 5¹⁰⁶ [i]