MinT - Best Known (15, 15+3, s)-Nets in Base 4

Best Known (15, 15+3, s)-Nets in Base 4

(15, 15+3, large)-Net over F₄ — Constructive and digital

Digital (15, 18, large)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁸, large, F₄, 3, 3), using
- appending kth column [i] based on linear OOA(4¹⁸, large, F₄, 2, 3), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4¹⁸, large, F₄, 3) (dual of [large, large−18, 4]-code), using
    - product of projective cap with (hyper)oval [i] based on linear OA(4¹⁶, 1850766, F₄, 3) (dual of [1850766, 1850750, 4]-code or 1850766-cap in PG(15,4)), using
      - product of projective cap with cap in AG(5,Â 4) [i] based on linear OA(4¹¹, 15423, F₄, 3) (dual of [15423, 15412, 4]-code or 15423-cap in PG(10,4)), using
        caps completed using a computer search [i]

(15, 15+3, large)-Net in Base 4 — Upper bound on s

There is no (15, 18, large)-net in base 4, because

1 times m-reduction [i] would yield (15, 17, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]