Best Known (125, 140, s)-Nets in Base 3
(125, 140, 683281)-Net over F3 — Constructive and digital
Digital (125, 140, 683281)-net over F3, using
- net defined by OOA [i] based on linear OOA(3140, 683281, F3, 15, 15) (dual of [(683281, 15), 10249075, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3140, 4782968, F3, 15) (dual of [4782968, 4782828, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(3140, 4782968, F3, 15) (dual of [4782968, 4782828, 16]-code), using
(125, 140, 1594322)-Net over F3 — Digital
Digital (125, 140, 1594322)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3140, 1594322, F3, 3, 15) (dual of [(1594322, 3), 4782826, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3140, 4782966, F3, 15) (dual of [4782966, 4782826, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3140, 4782968, F3, 15) (dual of [4782968, 4782828, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3140, 4782968, F3, 15) (dual of [4782968, 4782828, 16]-code), using
- OOA 3-folding [i] based on linear OA(3140, 4782966, F3, 15) (dual of [4782966, 4782826, 16]-code), using
(125, 140, large)-Net in Base 3 — Upper bound on s
There is no (125, 140, large)-net in base 3, because
- 13 times m-reduction [i] would yield (125, 127, large)-net in base 3, but