MinT - Best Known (79, 126, s)-Nets in Base 5

Best Known (79, 126, s)-Nets in Base 5

(79, 126, 252)-Net over F₅ — Constructive and digital

Digital (79, 126, 252)-net over F₅, using

12 times m-reduction [i] based on digital (79, 138, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 69, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(79, 126, 359)-Net over F₅ — Digital

Digital (79, 126, 359)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 126, 14813)-Net in Base 5 — Upper bound on s

There is no (79, 126, 14814)-net in base 5, because

1 times m-reduction [i] would yield (79, 125, 14814)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2353 056795 035687 559977 069520 669516 486987 978450 872555 852241 143639 633428 071211 425608 356505 > 5¹²⁵ [i]