MinT - Best Known (105−29, 105, s)-Nets in Base 5

Best Known (105−29, 105, s)-Nets in Base 5

(105−29, 105, 296)-Net over F₅ — Constructive and digital

Digital (76, 105, 296)-net over F₅, using

9 times m-reduction [i] based on digital (76, 114, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 57, 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]

(105−29, 105, 1194)-Net over F₅ — Digital

Digital (76, 105, 1194)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−29, 105, 235357)-Net in Base 5 — Upper bound on s

There is no (76, 105, 235358)-net in base 5, because

1 times m-reduction [i] would yield (76, 104, 235358)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 930549 925027 552127 730725 288471 038573 412780 617228 519554 501910 026645 897025 > 5¹⁰⁴ [i]