MinT - Best Known (1, 1+3, s)-Nets in Base 3

Best Known (1, 1+3, s)-Nets in Base 3

(1, 1+3, 10)-Net over F₃ — Constructive and digital

Digital (1, 4, 10)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁴, 10, F₃, 3, 3) (dual of [(10, 3), 26, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁴, 10, F₃, 2, 3) (dual of [(10, 2), 16, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
    - ovoid in PG(3,Â 3) [i]

(1, 1+3, 10)-Net in Base 3 — Upper bound on s

There is no (1, 4, 11)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴, 11, S₃, 3), but
- bound by Seiden [i]