MinT - Best Known (104−29, 104, s)-Nets in Base 5

Best Known (104−29, 104, s)-Nets in Base 5

(104−29, 104, 296)-Net over F₅ — Constructive and digital

Digital (75, 104, 296)-net over F₅, using

8 times m-reduction [i] based on digital (75, 112, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 56, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(104−29, 104, 1128)-Net over F₅ — Digital

Digital (75, 104, 1128)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(104−29, 104, 209796)-Net in Base 5 — Upper bound on s

There is no (75, 104, 209797)-net in base 5, because

1 times m-reduction [i] would yield (75, 103, 209797)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 986077 742344 303219 874581 010989 512125 286608 606482 204402 923598 337336 864105 > 5¹⁰³ [i]