MinT - Best Known (14−5, 14, s)-Nets in Base 16

Best Known (14−5, 14, s)-Nets in Base 16

Digital (9, 14, 65280)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16¹⁴, 65280, F₁₆, 5, 5) (dual of [(65280, 5), 326386, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(16¹⁴, 130561, F₁₆, 5) (dual of [130561, 130547, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
    - trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
      - a code by Danev and Olsson [i]

Digital (9, 14, 65281)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(16¹⁴, 65281, F₁₆, 2, 5) (dual of [(65281, 2), 130548, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
  - trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
    - a code by Danev and Olsson [i]

There is no (9, 14, 6327084)-net in base 16, because

1 times m-reduction [i] would yield (9, 13, 6327084)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 4503 599995 203271 > 16¹³ [i]