MinT - Best Known (91, 91+53, s)-Nets in Base 5

Best Known (91, 91+53, s)-Nets in Base 5

(91, 91+53, 296)-Net over F₅ — Constructive and digital

Digital (91, 144, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 72, 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]

(91, 91+53, 423)-Net over F₅ — Digital

Digital (91, 144, 423)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+53, 18412)-Net in Base 5 — Upper bound on s

There is no (91, 144, 18413)-net in base 5, because

1 times m-reduction [i] would yield (91, 143, 18413)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8970 578374 291192 487473 632790 092172 993687 728294 373226 314097 864854 979376 901498 290902 674998 005439 612857 > 5¹⁴³ [i]