Best Known (175, 175+22, s)-Nets in Base 3
(175, 175+22, 434815)-Net over F3 — Constructive and digital
Digital (175, 197, 434815)-net over F3, using
- net defined by OOA [i] based on linear OOA(3197, 434815, F3, 22, 22) (dual of [(434815, 22), 9565733, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3197, 4782965, F3, 22) (dual of [4782965, 4782768, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3197, 4782965, F3, 22) (dual of [4782965, 4782768, 23]-code), using
(175, 175+22, 956593)-Net over F3 — Digital
Digital (175, 197, 956593)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3197, 956593, F3, 5, 22) (dual of [(956593, 5), 4782768, 23]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3197, 4782965, F3, 22) (dual of [4782965, 4782768, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- OOA 5-folding [i] based on linear OA(3197, 4782965, F3, 22) (dual of [4782965, 4782768, 23]-code), using
(175, 175+22, large)-Net in Base 3 — Upper bound on s
There is no (175, 197, large)-net in base 3, because
- 20 times m-reduction [i] would yield (175, 177, large)-net in base 3, but