MinT - Best Known (95−20, 95, s)-Nets in Base 25

Best Known (95−20, 95, s)-Nets in Base 25

(95−20, 95, 39140)-Net over F₂₅ — Constructive and digital

Digital (75, 95, 39140)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (8, 18, 78)-net over F₂₅, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 5, 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 (3, 13, 52)-net over F₂₅, using
      - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
        a function field by GarcÃa and Quoos [i]
2. digital (57, 77, 39062)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25⁷⁷, 39062, F₂₅, 20, 20) (dual of [(39062, 20), 781163, 21]-NRT-code), using
    - OA 10-folding and stacking [i] based on linear OA(25⁷⁷, 390620, F₂₅, 20) (dual of [390620, 390543, 21]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁷⁷, 390625, F₂₅, 20) (dual of [390625, 390548, 21]-code), using
        an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

(95−20, 95, 3226306)-Net over F₂₅ — Digital

Digital (75, 95, 3226306)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−20, 95, large)-Net in Base 25 — Upper bound on s

There is no (75, 95, large)-net in base 25, because

18 times m-reduction [i] would yield (75, 77, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]

Best Known (95−20, 95, s)-Nets in Base 25

(95−20, 95, 39140)-Net over F25 — Constructive and digital

(95−20, 95, 3226306)-Net over F25 — Digital

(95−20, 95, large)-Net in Base 25 — Upper bound on s

(95−20, 95, 39140)-Net over F₂₅ — Constructive and digital

(95−20, 95, 3226306)-Net over F₂₅ — Digital