MinT - Best Known (74−49, 74, s)-Nets in Base 5

Best Known (74−49, 74, s)-Nets in Base 5

(74−49, 74, 51)-Net over F₅ — Constructive and digital

Digital (25, 74, 51)-net over F₅, using

t-expansion [i] based on digital (22, 74, 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]

(74−49, 74, 55)-Net over F₅ — Digital

Digital (25, 74, 55)-net over F₅, using

t-expansion [i] based on digital (23, 74, 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]

(74−49, 74, 310)-Net in Base 5 — Upper bound on s

There is no (25, 74, 311)-net in base 5, because

1 times m-reduction [i] would yield (25, 73, 311)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1104 559749 338791 456830 916498 966971 773960 582707 883425 > 5⁷³ [i]