Best Known (175−21, 175, s)-Nets in Base 3
(175−21, 175, 53148)-Net over F3 — Constructive and digital
Digital (154, 175, 53148)-net over F3, using
- net defined by OOA [i] based on linear OOA(3175, 53148, F3, 21, 21) (dual of [(53148, 21), 1115933, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3175, 531481, F3, 21) (dual of [531481, 531306, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3175, 531483, F3, 21) (dual of [531483, 531308, 22]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3175, 531483, F3, 21) (dual of [531483, 531308, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3175, 531481, F3, 21) (dual of [531481, 531306, 22]-code), using
(175−21, 175, 177161)-Net over F3 — Digital
Digital (154, 175, 177161)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3175, 177161, F3, 3, 21) (dual of [(177161, 3), 531308, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3175, 531483, F3, 21) (dual of [531483, 531308, 22]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- OOA 3-folding [i] based on linear OA(3175, 531483, F3, 21) (dual of [531483, 531308, 22]-code), using
(175−21, 175, large)-Net in Base 3 — Upper bound on s
There is no (154, 175, large)-net in base 3, because
- 19 times m-reduction [i] would yield (154, 156, large)-net in base 3, but