MinT - Best Known (88, 88+57, s)-Nets in Base 5

Best Known (88, 88+57, s)-Nets in Base 5

(88, 88+57, 252)-Net over F₅ — Constructive and digital

Digital (88, 145, 252)-net over F₅, using

t-expansion [i] based on digital (85, 145, 252)-net over F₅, using
- 5 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(88, 88+57, 331)-Net over F₅ — Digital

Digital (88, 145, 331)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+57, 11087)-Net in Base 5 — Upper bound on s

There is no (88, 145, 11088)-net in base 5, because

1 times m-reduction [i] would yield (88, 144, 11088)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44861 711182 834875 793125 535606 942144 896708 922399 327371 325186 574350 938951 284126 189384 650427 353021 476865 > 5¹⁴⁴ [i]