Best Known (177−23, 177, s)-Nets in Base 3
(177−23, 177, 16109)-Net over F3 — Constructive and digital
Digital (154, 177, 16109)-net over F3, using
- net defined by OOA [i] based on linear OOA(3177, 16109, F3, 23, 23) (dual of [(16109, 23), 370330, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3177, 177200, F3, 23) (dual of [177200, 177023, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3177, 177202, F3, 23) (dual of [177202, 177025, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(311, 55, F3, 5) (dual of [55, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3177, 177202, F3, 23) (dual of [177202, 177025, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3177, 177200, F3, 23) (dual of [177200, 177023, 24]-code), using
(177−23, 177, 62080)-Net over F3 — Digital
Digital (154, 177, 62080)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3177, 62080, F3, 2, 23) (dual of [(62080, 2), 123983, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3177, 88601, F3, 2, 23) (dual of [(88601, 2), 177025, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3177, 177202, F3, 23) (dual of [177202, 177025, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(311, 55, F3, 5) (dual of [55, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(3177, 177202, F3, 23) (dual of [177202, 177025, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(3177, 88601, F3, 2, 23) (dual of [(88601, 2), 177025, 24]-NRT-code), using
(177−23, 177, large)-Net in Base 3 — Upper bound on s
There is no (154, 177, large)-net in base 3, because
- 21 times m-reduction [i] would yield (154, 156, large)-net in base 3, but