Best Known (101, 118, s)-Nets in Base 3
(101, 118, 7385)-Net over F3 — Constructive and digital
Digital (101, 118, 7385)-net over F3, using
- 31 times duplication [i] based on digital (100, 117, 7385)-net over F3, using
- net defined by OOA [i] based on linear OOA(3117, 7385, F3, 17, 17) (dual of [(7385, 17), 125428, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3117, 59081, F3, 17) (dual of [59081, 58964, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3117, 59081, F3, 17) (dual of [59081, 58964, 18]-code), using
- net defined by OOA [i] based on linear OOA(3117, 7385, F3, 17, 17) (dual of [(7385, 17), 125428, 18]-NRT-code), using
(101, 118, 27134)-Net over F3 — Digital
Digital (101, 118, 27134)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3118, 27134, F3, 2, 17) (dual of [(27134, 2), 54150, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3118, 29543, F3, 2, 17) (dual of [(29543, 2), 58968, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3118, 59086, F3, 17) (dual of [59086, 58968, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using
- OOA 2-folding [i] based on linear OA(3118, 59086, F3, 17) (dual of [59086, 58968, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(3118, 29543, F3, 2, 17) (dual of [(29543, 2), 58968, 18]-NRT-code), using
(101, 118, large)-Net in Base 3 — Upper bound on s
There is no (101, 118, large)-net in base 3, because
- 15 times m-reduction [i] would yield (101, 103, large)-net in base 3, but