Best Known (127, 144, s)-Nets in Base 3
(127, 144, 199291)-Net over F3 — Constructive and digital
Digital (127, 144, 199291)-net over F3, using
- net defined by OOA [i] based on linear OOA(3144, 199291, F3, 17, 17) (dual of [(199291, 17), 3387803, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3144, 1594329, F3, 17) (dual of [1594329, 1594185, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3144, 1594336, F3, 17) (dual of [1594336, 1594192, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3144, 1594336, F3, 17) (dual of [1594336, 1594192, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3144, 1594329, F3, 17) (dual of [1594329, 1594185, 18]-code), using
(127, 144, 423930)-Net over F3 — Digital
Digital (127, 144, 423930)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3144, 423930, F3, 3, 17) (dual of [(423930, 3), 1271646, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3144, 531445, F3, 3, 17) (dual of [(531445, 3), 1594191, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3144, 1594335, F3, 17) (dual of [1594335, 1594191, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3144, 1594336, F3, 17) (dual of [1594336, 1594192, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3144, 1594336, F3, 17) (dual of [1594336, 1594192, 18]-code), using
- OOA 3-folding [i] based on linear OA(3144, 1594335, F3, 17) (dual of [1594335, 1594191, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(3144, 531445, F3, 3, 17) (dual of [(531445, 3), 1594191, 18]-NRT-code), using
(127, 144, large)-Net in Base 3 — Upper bound on s
There is no (127, 144, large)-net in base 3, because
- 15 times m-reduction [i] would yield (127, 129, large)-net in base 3, but