MinT - Best Known (26, 26+79, s)-Nets in Base 5

Best Known (26, 26+79, s)-Nets in Base 5

(26, 26+79, 51)-Net over F₅ — Constructive and digital

Digital (26, 105, 51)-net over F₅, using

t-expansion [i] based on digital (22, 105, 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+79, 55)-Net over F₅ — Digital

Digital (26, 105, 55)-net over F₅, using

t-expansion [i] based on digital (23, 105, 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+79, 253)-Net in Base 5 — Upper bound on s

There is no (26, 105, 254)-net in base 5, because

1 times m-reduction [i] would yield (26, 104, 254)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 195298 962675 506945 544169 982982 930059 347759 225642 935342 661479 566587 449625 > 5¹⁰⁴ [i]