MinT - Best Known (90, 90+57, s)-Nets in Base 5

Best Known (90, 90+57, s)-Nets in Base 5

(90, 90+57, 252)-Net over F₅ — Constructive and digital

Digital (90, 147, 252)-net over F₅, using

t-expansion [i] based on digital (85, 147, 252)-net over F₅, using
- 3 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]

(90, 90+57, 352)-Net over F₅ — Digital

Digital (90, 147, 352)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+57, 12441)-Net in Base 5 — Upper bound on s

There is no (90, 147, 12442)-net in base 5, because

1 times m-reduction [i] would yield (90, 146, 12442)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 123238 390484 727231 114467 194583 645220 001411 659679 619904 890062 939538 887124 910123 393539 431799 426168 983745 > 5¹⁴⁶ [i]