MinT - Best Known (84−55, 84, s)-Nets in Base 5

Best Known (84−55, 84, s)-Nets in Base 5

(84−55, 84, 51)-Net over F₅ — Constructive and digital

Digital (29, 84, 51)-net over F₅, using

t-expansion [i] based on digital (22, 84, 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]

(84−55, 84, 56)-Net over F₅ — Digital

Digital (29, 84, 56)-net over F₅, using

net from sequence [i] based on digital (29, 55)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 29 and N(F) ≥ 56, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(84−55, 84, 365)-Net in Base 5 — Upper bound on s

There is no (29, 84, 366)-net in base 5, because

1 times m-reduction [i] would yield (29, 83, 366)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10917 328915 171397 325359 677239 554233 839287 657465 172446 770905 > 5⁸³ [i]