MinT - Best Known (79, 79+69, s)-Nets in Base 5

Best Known (79, 79+69, s)-Nets in Base 5

(79, 79+69, 132)-Net over F₅ — Constructive and digital

Digital (79, 148, 132)-net over F₅, using

2 times m-reduction [i] based on digital (79, 150, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 75, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(79, 79+69, 183)-Net over F₅ — Digital

Digital (79, 148, 183)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+69, 3534)-Net in Base 5 — Upper bound on s

There is no (79, 148, 3535)-net in base 5, because

1 times m-reduction [i] would yield (79, 147, 3535)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 609389 670946 578518 328052 146849 940179 203032 662646 565485 503139 485354 650663 862620 616656 601801 061113 419641 > 5¹⁴⁷ [i]