Best Known (217, 247, s)-Nets in Base 3
(217, 247, 35432)-Net over F3 — Constructive and digital
Digital (217, 247, 35432)-net over F3, using
- net defined by OOA [i] based on linear OOA(3247, 35432, F3, 30, 30) (dual of [(35432, 30), 1062713, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3247, 531480, F3, 30) (dual of [531480, 531233, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3247, 531483, F3, 30) (dual of [531483, 531236, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3241, 531441, F3, 31) (dual of [531441, 531200, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3205, 531441, F3, 26) (dual of [531441, 531236, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3247, 531483, F3, 30) (dual of [531483, 531236, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3247, 531480, F3, 30) (dual of [531480, 531233, 31]-code), using
(217, 247, 158414)-Net over F3 — Digital
Digital (217, 247, 158414)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3247, 158414, F3, 3, 30) (dual of [(158414, 3), 474995, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3247, 177161, F3, 3, 30) (dual of [(177161, 3), 531236, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3247, 531483, F3, 30) (dual of [531483, 531236, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3241, 531441, F3, 31) (dual of [531441, 531200, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3205, 531441, F3, 26) (dual of [531441, 531236, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- OOA 3-folding [i] based on linear OA(3247, 531483, F3, 30) (dual of [531483, 531236, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(3247, 177161, F3, 3, 30) (dual of [(177161, 3), 531236, 31]-NRT-code), using
(217, 247, large)-Net in Base 3 — Upper bound on s
There is no (217, 247, large)-net in base 3, because
- 28 times m-reduction [i] would yield (217, 219, large)-net in base 3, but