MinT - Best Known (8, 13, s)-Nets in Base 7

Best Known (8, 13, s)-Nets in Base 7

(8, 13, 1176)-Net over F₇ — Constructive and digital

Digital (8, 13, 1176)-net over F₇, using

net defined by OOA [i] based on linear OOA(7¹³, 1176, F₇, 5, 5) (dual of [(1176, 5), 5867, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(7¹³, 2353, F₇, 5) (dual of [2353, 2340, 6]-code), using
  - base reduction for projective spaces (embedding PG(6,49) in PG(12,7)) [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
    - a code by Danev and Olsson [i]

(8, 13, 27729)-Net in Base 7 — Upper bound on s

There is no (8, 13, 27730)-net in base 7, because

1 times m-reduction [i] would yield (8, 12, 27730)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 13841 984101 > 7¹² [i]