MinT - Best Known (9, 14, s)-Nets in Base 5

Best Known (9, 14, s)-Nets in Base 5

Digital (9, 14, 600)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹⁴, 600, F₅, 5, 5) (dual of [(600, 5), 2986, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(5¹⁴, 1201, F₅, 5) (dual of [1201, 1187, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
    - trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
      - a code by Danev and Olsson [i]

Digital (9, 14, 601)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5¹⁴, 601, F₅, 2, 5) (dual of [(601, 2), 1188, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
  - trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
    - a code by Danev and Olsson [i]

There is no (9, 14, 12352)-net in base 5, because

1 times m-reduction [i] would yield (9, 13, 12352)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1220 772865 > 5¹³ [i]