MinT - Best Known (91, 91+51, s)-Nets in Base 5

Best Known (91, 91+51, s)-Nets in Base 5

(91, 91+51, 296)-Net over F₅ — Constructive and digital

Digital (91, 142, 296)-net over F₅, using

2 times m-reduction [i] based on 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+51, 461)-Net over F₅ — Digital

Digital (91, 142, 461)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+51, 22253)-Net in Base 5 — Upper bound on s

There is no (91, 142, 22254)-net in base 5, because

1 times m-reduction [i] would yield (91, 141, 22254)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 358 883758 318293 426767 363702 676764 321355 729795 309680 502343 699375 429813 268293 778510 188051 384881 004985 > 5¹⁴¹ [i]