MinT - Best Known (91, 91+57, s)-Nets in Base 5

Best Known (91, 91+57, s)-Nets in Base 5

(91, 91+57, 252)-Net over F₅ — Constructive and digital

Digital (91, 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]

(91, 91+57, 363)-Net over F₅ — Digital

Digital (91, 148, 363)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+57, 13178)-Net in Base 5 — Upper bound on s

There is no (91, 148, 13179)-net in base 5, because

1 times m-reduction [i] would yield (91, 147, 13179)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 612261 144087 749485 767164 086006 690895 361893 528086 001354 337423 223695 982487 717079 197984 761383 432825 373457 > 5¹⁴⁷ [i]