MinT - Best Known (88, 88+41, s)-Nets in Base 5

Best Known (88, 88+41, s)-Nets in Base 5

(88, 88+41, 296)-Net over F₅ — Constructive and digital

Digital (88, 129, 296)-net over F₅, using

9 times m-reduction [i] based on digital (88, 138, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 69, 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]

(88, 88+41, 728)-Net over F₅ — Digital

Digital (88, 129, 728)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+41, 61737)-Net in Base 5 — Upper bound on s

There is no (88, 129, 61738)-net in base 5, because

1 times m-reduction [i] would yield (88, 128, 61738)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 293877 220458 278223 487379 626624 700653 206062 094930 052242 401887 462518 071347 357480 183619 961665 > 5¹²⁸ [i]