MinT - Best Known (89, 89+61, s)-Nets in Base 5

Best Known (89, 89+61, s)-Nets in Base 5

(89, 89+61, 252)-Net over F₅ — Constructive and digital

Digital (89, 150, 252)-net over F₅, using

t-expansion [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]

(89, 89+61, 302)-Net over F₅ — Digital

Digital (89, 150, 302)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+61, 8896)-Net in Base 5 — Upper bound on s

There is no (89, 150, 8897)-net in base 5, because

1 times m-reduction [i] would yield (89, 149, 8897)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 474086 914362 062122 274566 564856 386413 180151 940362 977330 936757 062016 678776 328509 657216 845454 599593 695145 > 5¹⁴⁹ [i]