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

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

Digital (9, 14, 6480)-net over F₉, using

net defined by OOA [i] based on linear OOA(9¹⁴, 6480, F₉, 5, 5) (dual of [(6480, 5), 32386, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(9¹⁴, 12961, F₉, 5) (dual of [12961, 12947, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
    - trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
      - a code by Danev and Olsson [i]

Digital (9, 14, 6481)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(9¹⁴, 6481, F₉, 2, 5) (dual of [(6481, 2), 12948, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
  - trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
    - a code by Danev and Olsson [i]

There is no (9, 14, 281839)-net in base 9, because

1 times m-reduction [i] would yield (9, 13, 281839)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 541876 629745 > 9¹³ [i]