MinT - Best Known (5−3, 5, s)-Nets in Base 8

Best Known (5−3, 5, s)-Nets in Base 8

(5−3, 5, 208)-Net over F₈ — Constructive and digital

Digital (2, 5, 208)-net over F₈, using

net defined by OOA [i] based on linear OOA(8⁵, 208, F₈, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
    - caps completed using a computer search [i]

(5−3, 5, 493)-Net over F₈ — Upper bound on s (digital)

There is no digital (2, 5, 494)-net over F₈, because

extracting embedded orthogonal array [i] would yield linear OA(8⁵, 494, F₈, 3) (dual of [494, 489, 4]-code or 494-cap in PG(4,8)), but
- bound for caps in PG(4,Â b) [i]

(5−3, 5, 584)-Net in Base 8 — Upper bound on s

There is no (2, 5, 585)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵, 585, S₈, 3), but
- Boseâ€“Bush bound for OAs with strength 3 [i]