Best Known (100, 100+10, s)-Nets in Base 3
(100, 100+10, 1678087)-Net over F3 — Constructive and digital
Digital (100, 110, 1678087)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (14, 19, 367)-net over F3, using
- net defined by OOA [i] based on linear OOA(319, 367, F3, 5, 5) (dual of [(367, 5), 1816, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(319, 735, F3, 5) (dual of [735, 716, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(319, 729, F3, 5) (dual of [729, 710, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(313, 729, F3, 4) (dual of [729, 716, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(319, 735, F3, 5) (dual of [735, 716, 6]-code), using
- net defined by OOA [i] based on linear OOA(319, 367, F3, 5, 5) (dual of [(367, 5), 1816, 6]-NRT-code), using
- digital (81, 91, 1677720)-net over F3, using
- net defined by OOA [i] based on linear OOA(391, 1677720, F3, 10, 10) (dual of [(1677720, 10), 16777109, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
- net defined by OOA [i] based on linear OOA(391, 1677720, F3, 10, 10) (dual of [(1677720, 10), 16777109, 11]-NRT-code), using
- digital (14, 19, 367)-net over F3, using
(100, 100+10, 5962613)-Net over F3 — Digital
Digital (100, 110, 5962613)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3110, 5962613, F3, 10) (dual of [5962613, 5962503, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3110, large, F3, 10) (dual of [large, large−110, 11]-code), using
- 19 times code embedding in larger space [i] based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 19 times code embedding in larger space [i] based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3110, large, F3, 10) (dual of [large, large−110, 11]-code), using
(100, 100+10, large)-Net in Base 3 — Upper bound on s
There is no (100, 110, large)-net in base 3, because
- 8 times m-reduction [i] would yield (100, 102, large)-net in base 3, but