Best Known (86, 102, s)-Nets in Base 3
(86, 102, 7382)-Net over F3 — Constructive and digital
Digital (86, 102, 7382)-net over F3, using
- net defined by OOA [i] based on linear OOA(3102, 7382, F3, 16, 16) (dual of [(7382, 16), 118010, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3102, 59056, F3, 16) (dual of [59056, 58954, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3102, 59060, F3, 16) (dual of [59060, 58958, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 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(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3102, 59060, F3, 16) (dual of [59060, 58958, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3102, 59056, F3, 16) (dual of [59056, 58954, 17]-code), using
(86, 102, 19686)-Net over F3 — Digital
Digital (86, 102, 19686)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3102, 19686, F3, 3, 16) (dual of [(19686, 3), 58956, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3102, 59058, F3, 16) (dual of [59058, 58956, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3102, 59060, F3, 16) (dual of [59060, 58958, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 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(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3102, 59060, F3, 16) (dual of [59060, 58958, 17]-code), using
- OOA 3-folding [i] based on linear OA(3102, 59058, F3, 16) (dual of [59058, 58956, 17]-code), using
(86, 102, 2280103)-Net in Base 3 — Upper bound on s
There is no (86, 102, 2280104)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4 638399 187110 147855 249279 232660 246154 446244 850945 > 3102 [i]