MinT - Best Known (115−33, 115, s)-Nets in Base 5

Best Known (115−33, 115, s)-Nets in Base 5

(115−33, 115, 296)-Net over F₅ — Constructive and digital

Digital (82, 115, 296)-net over F₅, using

11 times m-reduction [i] based on digital (82, 126, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 63, 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]

(115−33, 115, 1055)-Net over F₅ — Digital

Digital (82, 115, 1055)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−33, 115, 162408)-Net in Base 5 — Upper bound on s

There is no (82, 115, 162409)-net in base 5, because

1 times m-reduction [i] would yield (82, 114, 162409)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 149717 610468 005056 746497 400279 696330 356593 009550 589497 055993 938578 510351 950785 > 5¹¹⁴ [i]