MinT - Best Known (5−3, 5, s)-Nets in Base 9

Best Known (5−3, 5, s)-Nets in Base 9

(5−3, 5, 212)-Net over F₉ — Constructive and digital

Digital (2, 5, 212)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁵, 212, F₉, 3, 3) (dual of [(212, 3), 631, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(9⁵, 212, F₉, 2, 3) (dual of [(212, 2), 419, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁵, 212, F₉, 3) (dual of [212, 207, 4]-code or 212-cap in PG(4,9)), using
    - caps completed using a computer search [i]

(5−3, 5, 703)-Net over F₉ — Upper bound on s (digital)

There is no digital (2, 5, 704)-net over F₉, because

extracting embedded orthogonal array [i] would yield linear OA(9⁵, 704, F₉, 3) (dual of [704, 699, 4]-code or 704-cap in PG(4,9)), but
- a result by Gronchi and Heim [i]

(5−3, 5, 819)-Net in Base 9 — Upper bound on s

There is no (2, 5, 820)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵, 820, S₉, 3), but
- Boseâ€“Bush bound for OAs with strength 3 [i]