MinT - Best Known (144−49, 144, s)-Nets in Base 5

Best Known (144−49, 144, s)-Nets in Base 5

(144−49, 144, 296)-Net over F₅ — Constructive and digital

Digital (95, 144, 296)-net over F₅, using

t-expansion [i] based on digital (94, 144, 296)-net over F₅, using
- 6 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]

(144−49, 144, 586)-Net over F₅ — Digital

Digital (95, 144, 586)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−49, 144, 35792)-Net in Base 5 — Upper bound on s

There is no (95, 144, 35793)-net in base 5, because

1 times m-reduction [i] would yield (95, 143, 35793)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8973 925553 359698 802996 283677 906501 848514 797014 476030 914622 211957 801520 169175 678749 940236 494651 435425 > 5¹⁴³ [i]