MinT - Best Known (13−5, 13, s)-Nets in Base 8

Best Known (13−5, 13, s)-Nets in Base 8

(13−5, 13, 2016)-Net over F₈ — Constructive and digital

Digital (8, 13, 2016)-net over F₈, using

net defined by OOA [i] based on linear OOA(8¹³, 2016, F₈, 5, 5) (dual of [(2016, 5), 10067, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8¹³, 4033, F₈, 5) (dual of [4033, 4020, 6]-code), using
  - base reduction for projective spaces (embedding PG(6,64) in PG(12,8)) [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
    - a code by Danev and Olsson [i]

(13−5, 13, 52960)-Net in Base 8 — Upper bound on s

There is no (8, 13, 52961)-net in base 8, because

1 times m-reduction [i] would yield (8, 12, 52961)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 68721 293264 > 8¹² [i]