Best Known (158, 158+26, s)-Nets in Base 4
(158, 158+26, 20168)-Net over F4 — Constructive and digital
Digital (158, 184, 20168)-net over F4, using
- 45 times duplication [i] based on digital (153, 179, 20168)-net over F4, using
- net defined by OOA [i] based on linear OOA(4179, 20168, F4, 26, 26) (dual of [(20168, 26), 524189, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4179, 262184, F4, 26) (dual of [262184, 262005, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4179, 262184, F4, 26) (dual of [262184, 262005, 27]-code), using
- net defined by OOA [i] based on linear OOA(4179, 20168, F4, 26, 26) (dual of [(20168, 26), 524189, 27]-NRT-code), using
(158, 158+26, 131097)-Net over F4 — Digital
Digital (158, 184, 131097)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4184, 131097, F4, 2, 26) (dual of [(131097, 2), 262010, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4184, 262194, F4, 26) (dual of [262194, 262010, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4179, 262189, F4, 22) (dual of [262189, 262010, 23]-code), using Gilbert–Varšamov bound and bm = 4179 > Vbs−1(k−1) = 126 396544 334049 441557 413334 981116 218821 911827 430276 105244 830395 752847 716546 525539 461079 944014 554075 133884 [i]
- linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reed–Solomon code RSe(2,4) [i]
- Simplex code S(2,4) [i]
- linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- construction X with Varšamov bound [i] based on
- OOA 2-folding [i] based on linear OA(4184, 262194, F4, 26) (dual of [262194, 262010, 27]-code), using
(158, 158+26, large)-Net in Base 4 — Upper bound on s
There is no (158, 184, large)-net in base 4, because
- 24 times m-reduction [i] would yield (158, 160, large)-net in base 4, but