Best Known (121, 143, s)-Nets in Base 9
(121, 143, 434819)-Net over F9 — Constructive and digital
Digital (121, 143, 434819)-net over F9, using
- 92 times duplication [i] based on digital (119, 141, 434819)-net over F9, using
- net defined by OOA [i] based on linear OOA(9141, 434819, F9, 22, 22) (dual of [(434819, 22), 9565877, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9141, 4783009, F9, 22) (dual of [4783009, 4782868, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9141, 4783011, F9, 22) (dual of [4783011, 4782870, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(97, 42, F9, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9141, 4783011, F9, 22) (dual of [4783011, 4782870, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(9141, 4783009, F9, 22) (dual of [4783009, 4782868, 23]-code), using
- net defined by OOA [i] based on linear OOA(9141, 434819, F9, 22, 22) (dual of [(434819, 22), 9565877, 23]-NRT-code), using
(121, 143, 4783015)-Net over F9 — Digital
Digital (121, 143, 4783015)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9143, 4783015, F9, 22) (dual of [4783015, 4782872, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9141, 4783011, F9, 22) (dual of [4783011, 4782870, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(97, 42, F9, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(9141, 4783013, F9, 21) (dual of [4783013, 4782872, 22]-code), using Gilbert–Varšamov bound and bm = 9141 > Vbs−1(k−1) = 18 607477 707935 013165 075750 689248 044807 559963 572580 979585 122447 462005 622181 938668 701710 896894 149022 771986 826389 514117 590437 936439 288481 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(9141, 4783011, F9, 22) (dual of [4783011, 4782870, 23]-code), using
- construction X with Varšamov bound [i] based on
(121, 143, large)-Net in Base 9 — Upper bound on s
There is no (121, 143, large)-net in base 9, because
- 20 times m-reduction [i] would yield (121, 123, large)-net in base 9, but