MinT - Best Known (13−5, 13, s)-Nets in Base 16

Best Known (13−5, 13, s)-Nets in Base 16

(13−5, 13, 32640)-Net over F₁₆ — Constructive and digital

Digital (8, 13, 32640)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16¹³, 32640, F₁₆, 5, 5) (dual of [(32640, 5), 163187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(16¹³, 65281, F₁₆, 5) (dual of [65281, 65268, 6]-code), using
  - base reduction for projective spaces (embedding PG(6,256) in PG(12,16)) [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
    - a code by Danev and Olsson [i]

(13−5, 13, 1581770)-Net in Base 16 — Upper bound on s

There is no (8, 13, 1581771)-net in base 16, because

1 times m-reduction [i] would yield (8, 12, 1581771)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 281 475168 751981 > 16¹² [i]