Best Known (183−28, 183, s)-Nets in Base 3
(183−28, 183, 4218)-Net over F3 — Constructive and digital
Digital (155, 183, 4218)-net over F3, using
- 31 times duplication [i] based on digital (154, 182, 4218)-net over F3, using
- net defined by OOA [i] based on linear OOA(3182, 4218, F3, 28, 28) (dual of [(4218, 28), 117922, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3182, 59052, F3, 28) (dual of [59052, 58870, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3182, 59060, F3, 28) (dual of [59060, 58878, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 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(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3182, 59060, F3, 28) (dual of [59060, 58878, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3182, 59052, F3, 28) (dual of [59052, 58870, 29]-code), using
- net defined by OOA [i] based on linear OOA(3182, 4218, F3, 28, 28) (dual of [(4218, 28), 117922, 29]-NRT-code), using
(183−28, 183, 18544)-Net over F3 — Digital
Digital (155, 183, 18544)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3183, 18544, F3, 3, 28) (dual of [(18544, 3), 55449, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3183, 19687, F3, 3, 28) (dual of [(19687, 3), 58878, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3183, 59061, F3, 28) (dual of [59061, 58878, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3182, 59060, F3, 28) (dual of [59060, 58878, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 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(27) ⊂ Ce(25) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3182, 59060, F3, 28) (dual of [59060, 58878, 29]-code), using
- OOA 3-folding [i] based on linear OA(3183, 59061, F3, 28) (dual of [59061, 58878, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(3183, 19687, F3, 3, 28) (dual of [(19687, 3), 58878, 29]-NRT-code), using
(183−28, 183, 5212943)-Net in Base 3 — Upper bound on s
There is no (155, 183, 5212944)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2056 791015 742869 559141 021608 889850 827271 102727 196630 550961 775938 087522 079123 691083 263841 > 3183 [i]