MinT - Best Known (120−41, 120, s)-Nets in Base 5

Best Known (120−41, 120, s)-Nets in Base 5

(120−41, 120, 296)-Net over F₅ — Constructive and digital

Digital (79, 120, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 60, 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]

(120−41, 120, 498)-Net over F₅ — Digital

Digital (79, 120, 498)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−41, 120, 29916)-Net in Base 5 — Upper bound on s

There is no (79, 120, 29917)-net in base 5, because

1 times m-reduction [i] would yield (79, 119, 29917)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 150537 295407 541260 953675 896152 018490 538317 675721 790803 333883 684631 253711 786993 805745 > 5¹¹⁹ [i]