Best Known (180−25, 180, s)-Nets in Base 3
(180−25, 180, 14763)-Net over F3 — Constructive and digital
Digital (155, 180, 14763)-net over F3, using
- 32 times duplication [i] based on digital (153, 178, 14763)-net over F3, using
- net defined by OOA [i] based on linear OOA(3178, 14763, F3, 25, 25) (dual of [(14763, 25), 368897, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3178, 177157, F3, 25) (dual of [177157, 176979, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3178, 177159, F3, 25) (dual of [177159, 176981, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3178, 177159, F3, 25) (dual of [177159, 176981, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3178, 177157, F3, 25) (dual of [177157, 176979, 26]-code), using
- net defined by OOA [i] based on linear OOA(3178, 14763, F3, 25, 25) (dual of [(14763, 25), 368897, 26]-NRT-code), using
(180−25, 180, 45575)-Net over F3 — Digital
Digital (155, 180, 45575)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3180, 45575, F3, 3, 25) (dual of [(45575, 3), 136545, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3180, 59053, F3, 3, 25) (dual of [(59053, 3), 176979, 26]-NRT-code), using
- 32 times duplication [i] based on linear OOA(3178, 59053, F3, 3, 25) (dual of [(59053, 3), 176981, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3178, 177159, F3, 25) (dual of [177159, 176981, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- OOA 3-folding [i] based on linear OA(3178, 177159, F3, 25) (dual of [177159, 176981, 26]-code), using
- 32 times duplication [i] based on linear OOA(3178, 59053, F3, 3, 25) (dual of [(59053, 3), 176981, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3180, 59053, F3, 3, 25) (dual of [(59053, 3), 176979, 26]-NRT-code), using
(180−25, 180, large)-Net in Base 3 — Upper bound on s
There is no (155, 180, large)-net in base 3, because
- 23 times m-reduction [i] would yield (155, 157, large)-net in base 3, but