MinT - Best Known (5−3, 5, s)-Nets in Base 2

Best Known (5−3, 5, s)-Nets in Base 2

(5−3, 5, 15)-Net over F₂ — Constructive and digital

Digital (2, 5, 15)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁵, 15, F₂, 3, 3) (dual of [(15, 3), 40, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(2⁵, 16, F₂, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
  - Reedâ€“Muller code RM(1,4) [i]
  - caps in base bÂ =Â 2 [i]

(5−3, 5, 15)-Net in Base 2 — Upper bound on s

There is no (2, 5, 16)-net in base 2, because

1 times m-reduction [i] would yield (2, 4, 16)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 17 > 2⁴ [i]