Best Known (171, 171+27, s)-Nets in Base 3
(171, 171+27, 13626)-Net over F3 — Constructive and digital
Digital (171, 198, 13626)-net over F3, using
- net defined by OOA [i] based on linear OOA(3198, 13626, F3, 27, 27) (dual of [(13626, 27), 367704, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3198, 177139, F3, 27) (dual of [177139, 176941, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3198, 177146, F3, 27) (dual of [177146, 176948, 28]-code), using
- 1 times truncation [i] based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 1 times truncation [i] based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3198, 177146, F3, 27) (dual of [177146, 176948, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3198, 177139, F3, 27) (dual of [177139, 176941, 28]-code), using
(171, 171+27, 52288)-Net over F3 — Digital
Digital (171, 198, 52288)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3198, 52288, F3, 3, 27) (dual of [(52288, 3), 156666, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3198, 59048, F3, 3, 27) (dual of [(59048, 3), 176946, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3198, 177144, F3, 27) (dual of [177144, 176946, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3198, 177146, F3, 27) (dual of [177146, 176948, 28]-code), using
- 1 times truncation [i] based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 1 times truncation [i] based on linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3198, 177146, F3, 27) (dual of [177146, 176948, 28]-code), using
- OOA 3-folding [i] based on linear OA(3198, 177144, F3, 27) (dual of [177144, 176946, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(3198, 59048, F3, 3, 27) (dual of [(59048, 3), 176946, 28]-NRT-code), using
(171, 171+27, large)-Net in Base 3 — Upper bound on s
There is no (171, 198, large)-net in base 3, because
- 25 times m-reduction [i] would yield (171, 173, large)-net in base 3, but