Best Known (46−8, 46, s)-Nets in Base 3
(46−8, 46, 4923)-Net over F3 — Constructive and digital
Digital (38, 46, 4923)-net over F3, using
- net defined by OOA [i] based on linear OOA(346, 4923, F3, 8, 8) (dual of [(4923, 8), 39338, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(346, 19692, F3, 8) (dual of [19692, 19646, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(346, 19683, F3, 8) (dual of [19683, 19637, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(337, 19683, F3, 7) (dual of [19683, 19646, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(346, 19692, F3, 8) (dual of [19692, 19646, 9]-code), using
(46−8, 46, 9846)-Net over F3 — Digital
Digital (38, 46, 9846)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(346, 9846, F3, 2, 8) (dual of [(9846, 2), 19646, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(346, 19692, F3, 8) (dual of [19692, 19646, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(346, 19683, F3, 8) (dual of [19683, 19637, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(337, 19683, F3, 7) (dual of [19683, 19646, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(346, 19692, F3, 8) (dual of [19692, 19646, 9]-code), using
(46−8, 46, 339557)-Net in Base 3 — Upper bound on s
There is no (38, 46, 339558)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8863 036022 648297 834249 > 346 [i]