MinT - Best Known (96, 96+33, s)-Nets in Base 5

Best Known (96, 96+33, s)-Nets in Base 5

(96, 96+33, 408)-Net over F₅ — Constructive and digital

Digital (96, 129, 408)-net over F₅, using

3 times m-reduction [i] based on digital (96, 132, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 66, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(96, 96+33, 2117)-Net over F₅ — Digital

Digital (96, 129, 2117)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+33, 664096)-Net in Base 5 — Upper bound on s

There is no (96, 129, 664097)-net in base 5, because

1 times m-reduction [i] would yield (96, 128, 664097)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 293876 520023 969330 267926 819945 462539 861200 015380 671351 708623 454341 033883 548360 745577 562049 > 5¹²⁸ [i]