Best Known (143, 143+21, s)-Nets in Base 3
(143, 143+21, 17719)-Net over F3 — Constructive and digital
Digital (143, 164, 17719)-net over F3, using
- net defined by OOA [i] based on linear OOA(3164, 17719, F3, 21, 21) (dual of [(17719, 21), 371935, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3164, 177191, F3, 21) (dual of [177191, 177027, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3164, 177200, F3, 21) (dual of [177200, 177036, 22]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(39, 53, F3, 4) (dual of [53, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3164, 177200, F3, 21) (dual of [177200, 177036, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3164, 177191, F3, 21) (dual of [177191, 177027, 22]-code), using
(143, 143+21, 74318)-Net over F3 — Digital
Digital (143, 164, 74318)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3164, 74318, F3, 2, 21) (dual of [(74318, 2), 148472, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3164, 88600, F3, 2, 21) (dual of [(88600, 2), 177036, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3164, 177200, F3, 21) (dual of [177200, 177036, 22]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(39, 53, F3, 4) (dual of [53, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(3164, 177200, F3, 21) (dual of [177200, 177036, 22]-code), using
- discarding factors / shortening the dual code based on linear OOA(3164, 88600, F3, 2, 21) (dual of [(88600, 2), 177036, 22]-NRT-code), using
(143, 143+21, large)-Net in Base 3 — Upper bound on s
There is no (143, 164, large)-net in base 3, because
- 19 times m-reduction [i] would yield (143, 145, large)-net in base 3, but