Best Known (80, 94, s)-Nets in Base 3
(80, 94, 8437)-Net over F3 — Constructive and digital
Digital (80, 94, 8437)-net over F3, using
- 33 times duplication [i] based on digital (77, 91, 8437)-net over F3, using
- net defined by OOA [i] based on linear OOA(391, 8437, F3, 14, 14) (dual of [(8437, 14), 118027, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(391, 59059, F3, 14) (dual of [59059, 58968, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(391, 59049, F3, 14) (dual of [59049, 58958, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(381, 59049, F3, 13) (dual of [59049, 58968, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- OA 7-folding and stacking [i] based on linear OA(391, 59059, F3, 14) (dual of [59059, 58968, 15]-code), using
- net defined by OOA [i] based on linear OOA(391, 8437, F3, 14, 14) (dual of [(8437, 14), 118027, 15]-NRT-code), using
(80, 94, 24003)-Net over F3 — Digital
Digital (80, 94, 24003)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(394, 24003, F3, 2, 14) (dual of [(24003, 2), 47912, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(394, 29531, F3, 2, 14) (dual of [(29531, 2), 58968, 15]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(392, 29530, F3, 2, 14) (dual of [(29530, 2), 58968, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(392, 59060, F3, 14) (dual of [59060, 58968, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(391, 59059, F3, 14) (dual of [59059, 58968, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(391, 59049, F3, 14) (dual of [59049, 58958, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(381, 59049, F3, 13) (dual of [59049, 58968, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 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(391, 59059, F3, 14) (dual of [59059, 58968, 15]-code), using
- OOA 2-folding [i] based on linear OA(392, 59060, F3, 14) (dual of [59060, 58968, 15]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(392, 29530, F3, 2, 14) (dual of [(29530, 2), 58968, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(394, 29531, F3, 2, 14) (dual of [(29531, 2), 58968, 15]-NRT-code), using
(80, 94, 4314642)-Net in Base 3 — Upper bound on s
There is no (80, 94, 4314643)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 706 965278 449519 923797 798614 066058 963661 890883 > 394 [i]