MinT - Best Known (147−53, 147, s)-Nets in Base 5

Best Known (147−53, 147, s)-Nets in Base 5

(147−53, 147, 296)-Net over F₅ — Constructive and digital

Digital (94, 147, 296)-net over F₅, using

3 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 75, 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]

(147−53, 147, 467)-Net over F₅ — Digital

Digital (94, 147, 467)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−53, 147, 22174)-Net in Base 5 — Upper bound on s

There is no (94, 147, 22175)-net in base 5, because

1 times m-reduction [i] would yield (94, 146, 22175)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 122180 971500 029258 640874 401819 829116 271986 643087 142408 416381 985887 944256 000640 687213 582900 950357 563289 > 5¹⁴⁶ [i]