MinT - Best Known (78, 78+41, s)-Nets in Base 5

Best Known (78, 78+41, s)-Nets in Base 5

(78, 78+41, 252)-Net over F₅ — Constructive and digital

Digital (78, 119, 252)-net over F₅, using

17 times m-reduction [i] based on digital (78, 136, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 68, 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]

(78, 78+41, 477)-Net over F₅ — Digital

Digital (78, 119, 477)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+41, 27602)-Net in Base 5 — Upper bound on s

There is no (78, 119, 27603)-net in base 5, because

1 times m-reduction [i] would yield (78, 118, 27603)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30113 525160 471768 815645 167248 636658 084054 722604 420904 694412 275324 307385 059049 008945 > 5¹¹⁸ [i]