MinT - Best Known (95−20, 95, s)-Nets in Base 5

Best Known (95−20, 95, s)-Nets in Base 5

(95−20, 95, 408)-Net over F₅ — Constructive and digital

Digital (75, 95, 408)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (25, 35, 156)-net over F₅, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (2, 5, 52)-net over F₅, using
      - s-reduction based on digital (2, 5, 66)-net over F₅, using
        net defined by OOA [i] based on linear OOA(5⁵, 66, F₅, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
        caps completed using a computer search [i]
    2. digital (5, 10, 52)-net over F₅, using
      - s-reduction based on digital (5, 10, 68)-net over F₅, using
        linear code embedding found in a computer search [i]
    3. digital (10, 20, 52)-net over F₅, using
      - trace code for nets [i] based on digital (0, 10, 26)-net over F₂₅, using
        net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
2. digital (40, 60, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 30, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
        the Hermitian function field over F₂₅ [i]

(95−20, 95, 6204)-Net over F₅ — Digital

Digital (75, 95, 6204)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−20, 95, 4944595)-Net in Base 5 — Upper bound on s

There is no (75, 95, 4944596)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 524359 248433 082773 097462 364997 409276 714908 914763 055014 770476 483521 > 5⁹⁵ [i]

Best Known (95−20, 95, s)-Nets in Base 5

(95−20, 95, 408)-Net over F5 — Constructive and digital

(95−20, 95, 6204)-Net over F5 — Digital

(95−20, 95, 4944595)-Net in Base 5 — Upper bound on s

(95−20, 95, 408)-Net over F₅ — Constructive and digital

(95−20, 95, 6204)-Net over F₅ — Digital