MinT - Best Known (81, 81+37, s)-Nets in Base 5

Best Known (81, 81+37, s)-Nets in Base 5

(81, 81+37, 296)-Net over F₅ — Constructive and digital

Digital (81, 118, 296)-net over F₅, using

6 times m-reduction [i] based on digital (81, 124, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 62, 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]

(81, 81+37, 716)-Net over F₅ — Digital

Digital (81, 118, 716)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+37, 65961)-Net in Base 5 — Upper bound on s

There is no (81, 118, 65962)-net in base 5, because

1 times m-reduction [i] would yield (81, 117, 65962)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6019 603605 808210 378118 858697 436114 025700 331005 044422 016745 405731 053309 577865 657025 > 5¹¹⁷ [i]