MinT - Best Known (105−77, 105, s)-Nets in Base 5

Best Known (105−77, 105, s)-Nets in Base 5

(105−77, 105, 51)-Net over F₅ — Constructive and digital

Digital (28, 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]

(105−77, 105, 55)-Net over F₅ — Digital

Digital (28, 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]

(105−77, 105, 280)-Net in Base 5 — Upper bound on s

There is no (28, 105, 281)-net in base 5, because

1 times m-reduction [i] would yield (28, 104, 281)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 391002 909156 286714 054955 988396 439021 305345 008465 492699 638874 474963 391625 > 5¹⁰⁴ [i]