Best Known (175, 175+24, s)-Nets in Base 3
(175, 175+24, 44290)-Net over F3 — Constructive and digital
Digital (175, 199, 44290)-net over F3, using
- net defined by OOA [i] based on linear OOA(3199, 44290, F3, 24, 24) (dual of [(44290, 24), 1062761, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3199, 531480, F3, 24) (dual of [531480, 531281, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3199, 531483, F3, 24) (dual of [531483, 531284, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3199, 531483, F3, 24) (dual of [531483, 531284, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3199, 531480, F3, 24) (dual of [531480, 531281, 25]-code), using
(175, 175+24, 177161)-Net over F3 — Digital
Digital (175, 199, 177161)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3199, 177161, F3, 3, 24) (dual of [(177161, 3), 531284, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3199, 531483, F3, 24) (dual of [531483, 531284, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(24) ⊂ Ce(19) [i] based on
- OOA 3-folding [i] based on linear OA(3199, 531483, F3, 24) (dual of [531483, 531284, 25]-code), using
(175, 175+24, large)-Net in Base 3 — Upper bound on s
There is no (175, 199, large)-net in base 3, because
- 22 times m-reduction [i] would yield (175, 177, large)-net in base 3, but