MinT - Best Known (88−25, 88, s)-Nets in Base 5

Best Known (88−25, 88, s)-Nets in Base 5

(88−25, 88, 296)-Net over F₅ — Constructive and digital

Digital (63, 88, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 44, 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]

(88−25, 88, 908)-Net over F₅ — Digital

Digital (63, 88, 908)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−25, 88, 154457)-Net in Base 5 — Upper bound on s

There is no (63, 88, 154458)-net in base 5, because

1 times m-reduction [i] would yield (63, 87, 154458)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6 462411 366731 992634 762395 105382 301022 662996 210312 252341 303745 > 5⁸⁷ [i]