MinT - Best Known (68, 68+28, s)-Nets in Base 5

Best Known (68, 68+28, s)-Nets in Base 5

(68, 68+28, 296)-Net over F₅ — Constructive and digital

Digital (68, 96, 296)-net over F₅, using

2 times m-reduction [i] based on digital (68, 98, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 49, 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]

(68, 68+28, 848)-Net over F₅ — Digital

Digital (68, 96, 848)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+28, 93818)-Net in Base 5 — Upper bound on s

There is no (68, 96, 93819)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 622655 517909 902937 371296 825263 645484 684500 897547 367789 466015 194825 > 5⁹⁶ [i]