MinT - Best Known (113−35, 113, s)-Nets in Base 5

Best Known (113−35, 113, s)-Nets in Base 5

(113−35, 113, 296)-Net over F₅ — Constructive and digital

Digital (78, 113, 296)-net over F₅, using

5 times m-reduction [i] based on digital (78, 118, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 59, 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]

(113−35, 113, 729)-Net over F₅ — Digital

Digital (78, 113, 729)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−35, 113, 72242)-Net in Base 5 — Upper bound on s

There is no (78, 113, 72243)-net in base 5, because

1 times m-reduction [i] would yield (78, 112, 72243)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 926332 254699 544883 970370 521939 894335 341183 496853 632927 808942 542755 126154 298509 > 5¹¹² [i]