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

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

(13−5, 13, 300)-Net over F₅ — Constructive and digital

Digital (8, 13, 300)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹³, 300, F₅, 5, 5) (dual of [(300, 5), 1487, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(5¹³, 601, F₅, 5) (dual of [601, 588, 6]-code), using
  - base reduction for projective spaces (embedding PG(6,25) in PG(12,5)) [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
    - a code by Danev and Olsson [i]

(13−5, 13, 5523)-Net in Base 5 — Upper bound on s

There is no (8, 13, 5524)-net in base 5, because

1 times m-reduction [i] would yield (8, 12, 5524)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 244 204993 > 5¹² [i]