MinT - Best Known (4, 4+5, s)-Nets in Base 49

Best Known (4, 4+5, s)-Nets in Base 49

(4, 4+5, 1226)-Net over F₄₉ — Constructive and digital

Digital (4, 9, 1226)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 2, 50)-net over F₄₉, using
  - kÂ =Â 2 construction [i]
2. digital (2, 7, 1176)-net over F₄₉, using
  - net defined by OOA [i] based on linear OOA(49⁷, 1176, F₄₉, 5, 5) (dual of [(1176, 5), 5873, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
      - a code by Danev and Olsson [i]

(4, 4+5, 169846)-Net in Base 49 — Upper bound on s

There is no (4, 9, 169847)-net in base 49, because

1 times m-reduction [i] would yield (4, 8, 169847)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 33 233111 896225 > 49⁸ [i]