Best Known (92, 110, s)-Nets in Base 3
(92, 110, 2189)-Net over F3 — Constructive and digital
Digital (92, 110, 2189)-net over F3, using
- net defined by OOA [i] based on linear OOA(3110, 2189, F3, 18, 18) (dual of [(2189, 18), 39292, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3110, 19701, F3, 18) (dual of [19701, 19591, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3110, 19702, F3, 18) (dual of [19702, 19592, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3109, 19683, F3, 19) (dual of [19683, 19574, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(31, 19, F3, 1) (dual of [19, 18, 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(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3110, 19702, F3, 18) (dual of [19702, 19592, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(3110, 19701, F3, 18) (dual of [19701, 19591, 19]-code), using
(92, 110, 8736)-Net over F3 — Digital
Digital (92, 110, 8736)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3110, 8736, F3, 2, 18) (dual of [(8736, 2), 17362, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3110, 9851, F3, 2, 18) (dual of [(9851, 2), 19592, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3110, 19702, F3, 18) (dual of [19702, 19592, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3109, 19683, F3, 19) (dual of [19683, 19574, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(31, 19, F3, 1) (dual of [19, 18, 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(18) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(3110, 19702, F3, 18) (dual of [19702, 19592, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(3110, 9851, F3, 2, 18) (dual of [(9851, 2), 19592, 19]-NRT-code), using
(92, 110, 1406697)-Net in Base 3 — Upper bound on s
There is no (92, 110, 1406698)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 30432 552226 183146 221106 042103 029774 112316 300269 005829 > 3110 [i]