MinT - Best Known (102, 102+46, s)-Nets in Base 5

Best Known (102, 102+46, s)-Nets in Base 5

(102, 102+46, 400)-Net over F₅ — Constructive and digital

Digital (102, 148, 400)-net over F₅, using

t-expansion [i] based on digital (100, 148, 400)-net over F₅, using
- 2 times m-reduction [i] based on digital (100, 150, 400)-net over F₅, using
  - trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(102, 102+46, 899)-Net over F₅ — Digital

Digital (102, 148, 899)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+46, 74134)-Net in Base 5 — Upper bound on s

There is no (102, 148, 74135)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 033511 564791 041227 969135 249698 649423 215760 393024 371581 639899 130675 471290 714592 887003 293860 491602 958725 > 5¹⁴⁸ [i]