Best Known (46−5, 46, s)-Nets in Base 3
(46−5, 46, 4194301)-Net over F3 — Constructive and digital
Digital (41, 46, 4194301)-net over F3, using
- net defined by OOA [i] based on linear OOA(346, 4194301, F3, 5, 5) (dual of [(4194301, 5), 20971459, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(346, large, F3, 5) (dual of [large, large−46, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(346, large, F3, 5) (dual of [large, large−46, 6]-code), using
(46−5, 46, large)-Net over F3 — Digital
Digital (41, 46, large)-net over F3, using
- net defined by OOA [i] based on linear OOA(346, large, F3, 5, 5), using
- appending kth column [i] based on linear OOA(346, large, F3, 4, 5), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(346, large, F3, 5) (dual of [large, large−46, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(346, large, F3, 5) (dual of [large, large−46, 6]-code), using
- appending kth column [i] based on linear OOA(346, large, F3, 4, 5), using
(46−5, 46, large)-Net in Base 3 — Upper bound on s
There is no (41, 46, large)-net in base 3, because
- 3 times m-reduction [i] would yield (41, 43, large)-net in base 3, but