MinT - Best Known (88, 88+60, s)-Nets in Base 5

Best Known (88, 88+60, s)-Nets in Base 5

(88, 88+60, 252)-Net over F₅ — Constructive and digital

Digital (88, 148, 252)-net over F₅, using

t-expansion [i] based on digital (85, 148, 252)-net over F₅, using
- 2 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+60, 301)-Net over F₅ — Digital

Digital (88, 148, 301)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+60, 8430)-Net in Base 5 — Upper bound on s

There is no (88, 148, 8431)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 082395 915416 340976 718141 694997 246595 640114 948214 589051 665808 863137 040523 345405 132209 348455 298481 941897 > 5¹⁴⁸ [i]