MinT - Best Known (94−37, 94, s)-Nets in Base 5

Best Known (94−37, 94, s)-Nets in Base 5

(94−37, 94, 252)-Net over F₅ — Constructive and digital

Digital (57, 94, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 47, 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]

(94−37, 94, 7703)-Net in Base 5 — Upper bound on s

There is no (57, 94, 7704)-net in base 5, because

1 times m-reduction [i] would yield (57, 93, 7704)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 101112 253975 620451 606387 581181 778386 498188 097810 305636 267414 213505 > 5⁹³ [i]