MinT - Best Known (104−57, 104, s)-Nets in Base 5

Best Known (104−57, 104, s)-Nets in Base 5

(104−57, 104, 78)-Net over F₅ — Constructive and digital

Digital (47, 104, 78)-net over F₅, using

t-expansion [i] based on digital (38, 104, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(104−57, 104, 92)-Net over F₅ — Digital

Digital (47, 104, 92)-net over F₅, using

net from sequence [i] based on digital (47, 91)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(104−57, 104, 1031)-Net in Base 5 — Upper bound on s

There is no (47, 104, 1032)-net in base 5, because

1 times m-reduction [i] would yield (47, 103, 1032)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 986548 478324 632478 199796 753246 364844 770261 528874 073262 790119 606799 289345 > 5¹⁰³ [i]