MinT - Best Known (26, 26+77, s)-Nets in Base 5

Best Known (26, 26+77, s)-Nets in Base 5

(26, 26+77, 51)-Net over F₅ — Constructive and digital

Digital (26, 103, 51)-net over F₅, using

t-expansion [i] based on digital (22, 103, 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]

(26, 26+77, 55)-Net over F₅ — Digital

Digital (26, 103, 55)-net over F₅, using

t-expansion [i] based on digital (23, 103, 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]

(26, 26+77, 255)-Net in Base 5 — Upper bound on s

There is no (26, 103, 256)-net in base 5, because

1 times m-reduction [i] would yield (26, 102, 256)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 214265 021298 961742 697528 835539 010617 531012 891741 969290 926316 138750 234625 > 5¹⁰² [i]