MinT - Best Known (66, 66+35, s)-Nets in Base 5

Best Known (66, 66+35, s)-Nets in Base 5

(66, 66+35, 252)-Net over F₅ — Constructive and digital

Digital (66, 101, 252)-net over F₅, using

11 times m-reduction [i] based on digital (66, 112, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 56, 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]

(66, 66+35, 412)-Net over F₅ — Digital

Digital (66, 101, 412)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+35, 23186)-Net in Base 5 — Upper bound on s

There is no (66, 101, 23187)-net in base 5, because

1 times m-reduction [i] would yield (66, 100, 23187)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7888 740215 139295 458698 780994 685602 014845 844413 508904 544735 887289 370125 > 5¹⁰⁰ [i]