MinT - Best Known (85, 85+61, s)-Nets in Base 5

Best Known (85, 85+61, s)-Nets in Base 5

(85, 85+61, 252)-Net over F₅ — Constructive and digital

Digital (85, 146, 252)-net over F₅, using

4 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]

(85, 85+61, 267)-Net over F₅ — Digital

Digital (85, 146, 267)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+61, 7173)-Net in Base 5 — Upper bound on s

There is no (85, 146, 7174)-net in base 5, because

1 times m-reduction [i] would yield (85, 145, 7174)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224300 759219 491728 707096 201775 892711 709239 796321 417965 586864 659631 548677 610742 592128 288485 152944 581569 > 5¹⁴⁵ [i]