MinT - Best Known (115−49, 115, s)-Nets in Base 5

Best Known (115−49, 115, s)-Nets in Base 5

(115−49, 115, 132)-Net over F₅ — Constructive and digital

Digital (66, 115, 132)-net over F₅, using

9 times m-reduction [i] based on digital (66, 124, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 62, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(115−49, 115, 204)-Net over F₅ — Digital

Digital (66, 115, 204)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−49, 115, 5104)-Net in Base 5 — Upper bound on s

There is no (66, 115, 5105)-net in base 5, because

1 times m-reduction [i] would yield (66, 114, 5105)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 334544 202792 278073 481152 362372 372779 930280 380273 674121 760958 786202 185602 941345 > 5¹¹⁴ [i]