MinT - Best Known (147−43, 147, s)-Nets in Base 5

Best Known (147−43, 147, s)-Nets in Base 5

(147−43, 147, 408)-Net over F₅ — Constructive and digital

Digital (104, 147, 408)-net over F₅, using

1 times m-reduction [i] based on digital (104, 148, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 74, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(147−43, 147, 1175)-Net over F₅ — Digital

Digital (104, 147, 1175)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−43, 147, 156998)-Net in Base 5 — Upper bound on s

There is no (104, 147, 156999)-net in base 5, because

1 times m-reduction [i] would yield (104, 146, 156999)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 121079 279300 523863 725432 869342 121262 028758 271937 503582 688703 798007 594966 419274 866127 780471 194794 547917 > 5¹⁴⁶ [i]