MinT - Best Known (80−51, 80, s)-Nets in Base 5

Best Known (80−51, 80, s)-Nets in Base 5

(80−51, 80, 51)-Net over F₅ — Constructive and digital

Digital (29, 80, 51)-net over F₅, using

t-expansion [i] based on digital (22, 80, 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]

(80−51, 80, 56)-Net over F₅ — Digital

Digital (29, 80, 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]

(80−51, 80, 393)-Net in Base 5 — Upper bound on s

There is no (29, 80, 394)-net in base 5, because

1 times m-reduction [i] would yield (29, 79, 394)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 17 075499 942200 006386 936366 475555 073185 599771 393257 599785 > 5⁷⁹ [i]