MinT - Best Known (76, 76+49, s)-Nets in Base 5

Best Known (76, 76+49, s)-Nets in Base 5

(76, 76+49, 252)-Net over F₅ — Constructive and digital

Digital (76, 125, 252)-net over F₅, using

7 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 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]

(76, 76+49, 295)-Net over F₅ — Digital

Digital (76, 125, 295)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+49, 9997)-Net in Base 5 — Upper bound on s

There is no (76, 125, 9998)-net in base 5, because

1 times m-reduction [i] would yield (76, 124, 9998)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 470 831951 198303 638748 527247 671060 292915 594540 669867 622979 609065 011828 666496 835768 324225 > 5¹²⁴ [i]