MinT - Best Known (130−46, 130, s)-Nets in Base 5

Best Known (130−46, 130, s)-Nets in Base 5

(130−46, 130, 296)-Net over F₅ — Constructive and digital

Digital (84, 130, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 65, 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]

(130−46, 130, 457)-Net over F₅ — Digital

Digital (84, 130, 457)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−46, 130, 21025)-Net in Base 5 — Upper bound on s

There is no (84, 130, 21026)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 349207 181832 028474 108021 341191 451073 031992 813791 584927 070720 797776 323084 106540 992572 934825 > 5¹³⁰ [i]