Best Known (173−26, 173, s)-Nets in Base 4
(173−26, 173, 20165)-Net over F4 — Constructive and digital
Digital (147, 173, 20165)-net over F4, using
- 41 times duplication [i] based on digital (146, 172, 20165)-net over F4, using
- net defined by OOA [i] based on linear OOA(4172, 20165, F4, 26, 26) (dual of [(20165, 26), 524118, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4172, 262145, F4, 26) (dual of [262145, 261973, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4172, 262153, F4, 26) (dual of [262153, 261981, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4172, 262153, F4, 26) (dual of [262153, 261981, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4172, 262145, F4, 26) (dual of [262145, 261973, 27]-code), using
- net defined by OOA [i] based on linear OOA(4172, 20165, F4, 26, 26) (dual of [(20165, 26), 524118, 27]-NRT-code), using
(173−26, 173, 94067)-Net over F4 — Digital
Digital (147, 173, 94067)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4173, 94067, F4, 2, 26) (dual of [(94067, 2), 187961, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4173, 131077, F4, 2, 26) (dual of [(131077, 2), 261981, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4173, 262154, F4, 26) (dual of [262154, 261981, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4172, 262153, F4, 26) (dual of [262153, 261981, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4172, 262153, F4, 26) (dual of [262153, 261981, 27]-code), using
- OOA 2-folding [i] based on linear OA(4173, 262154, F4, 26) (dual of [262154, 261981, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(4173, 131077, F4, 2, 26) (dual of [(131077, 2), 261981, 27]-NRT-code), using
(173−26, 173, large)-Net in Base 4 — Upper bound on s
There is no (147, 173, large)-net in base 4, because
- 24 times m-reduction [i] would yield (147, 149, large)-net in base 4, but