MinT - Best Known (81, 81+49, s)-Nets in Base 5

Best Known (81, 81+49, s)-Nets in Base 5

(81, 81+49, 252)-Net over F₅ — Constructive and digital

Digital (81, 130, 252)-net over F₅, using

12 times m-reduction [i] based on digital (81, 142, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 71, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(81, 81+49, 354)-Net over F₅ — Digital

Digital (81, 130, 354)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+49, 13986)-Net in Base 5 — Upper bound on s

There is no (81, 130, 13987)-net in base 5, because

1 times m-reduction [i] would yield (81, 129, 13987)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 469436 617406 027870 113364 801067 243668 722612 855564 195765 065126 368528 517300 646025 462178 763425 > 5¹²⁹ [i]