Best Known (154−21, 154, s)-Nets in Base 3
(154−21, 154, 17714)-Net over F3 — Constructive and digital
Digital (133, 154, 17714)-net over F3, using
- net defined by OOA [i] based on linear OOA(3154, 17714, F3, 21, 21) (dual of [(17714, 21), 371840, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3154, 177141, F3, 21) (dual of [177141, 176987, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3154, 177146, F3, 21) (dual of [177146, 176992, 22]-code), using
- 1 times truncation [i] based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 1 times truncation [i] based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3154, 177146, F3, 21) (dual of [177146, 176992, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3154, 177141, F3, 21) (dual of [177141, 176987, 22]-code), using
(154−21, 154, 59048)-Net over F3 — Digital
Digital (133, 154, 59048)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3154, 59048, F3, 3, 21) (dual of [(59048, 3), 176990, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3154, 177144, F3, 21) (dual of [177144, 176990, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3154, 177146, F3, 21) (dual of [177146, 176992, 22]-code), using
- 1 times truncation [i] based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 1 times truncation [i] based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3154, 177146, F3, 21) (dual of [177146, 176992, 22]-code), using
- OOA 3-folding [i] based on linear OA(3154, 177144, F3, 21) (dual of [177144, 176990, 22]-code), using
(154−21, 154, large)-Net in Base 3 — Upper bound on s
There is no (133, 154, large)-net in base 3, because
- 19 times m-reduction [i] would yield (133, 135, large)-net in base 3, but