Best Known (93−14, 93, s)-Nets in Base 4
(93−14, 93, 37450)-Net over F4 — Constructive and digital
Digital (79, 93, 37450)-net over F4, using
- 42 times duplication [i] based on digital (77, 91, 37450)-net over F4, using
- net defined by OOA [i] based on linear OOA(491, 37450, F4, 14, 14) (dual of [(37450, 14), 524209, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(491, 262150, F4, 14) (dual of [262150, 262059, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 262153, F4, 14) (dual of [262153, 262062, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(491, 262144, F4, 14) (dual of [262144, 262053, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(491, 262153, F4, 14) (dual of [262153, 262062, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(491, 262150, F4, 14) (dual of [262150, 262059, 15]-code), using
- net defined by OOA [i] based on linear OOA(491, 37450, F4, 14, 14) (dual of [(37450, 14), 524209, 15]-NRT-code), using
(93−14, 93, 131077)-Net over F4 — Digital
Digital (79, 93, 131077)-net over F4, using
- 41 times duplication [i] based on digital (78, 92, 131077)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(492, 131077, F4, 2, 14) (dual of [(131077, 2), 262062, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(492, 262154, F4, 14) (dual of [262154, 262062, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(491, 262153, F4, 14) (dual of [262153, 262062, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(491, 262144, F4, 14) (dual of [262144, 262053, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(491, 262153, F4, 14) (dual of [262153, 262062, 15]-code), using
- OOA 2-folding [i] based on linear OA(492, 262154, F4, 14) (dual of [262154, 262062, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(492, 131077, F4, 2, 14) (dual of [(131077, 2), 262062, 15]-NRT-code), using
(93−14, 93, large)-Net in Base 4 — Upper bound on s
There is no (79, 93, large)-net in base 4, because
- 12 times m-reduction [i] would yield (79, 81, large)-net in base 4, but