Best Known (102, 117, s)-Nets in Base 3
(102, 117, 25312)-Net over F3 — Constructive and digital
Digital (102, 117, 25312)-net over F3, using
- net defined by OOA [i] based on linear OOA(3117, 25312, F3, 15, 15) (dual of [(25312, 15), 379563, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3117, 177185, F3, 15) (dual of [177185, 177068, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 177186, F3, 15) (dual of [177186, 177069, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(378, 177147, F3, 11) (dual of [177147, 177069, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-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(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3117, 177186, F3, 15) (dual of [177186, 177069, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3117, 177185, F3, 15) (dual of [177185, 177068, 16]-code), using
(102, 117, 88593)-Net over F3 — Digital
Digital (102, 117, 88593)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3117, 88593, F3, 2, 15) (dual of [(88593, 2), 177069, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3117, 177186, F3, 15) (dual of [177186, 177069, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(378, 177147, F3, 11) (dual of [177147, 177069, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-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(15) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(3117, 177186, F3, 15) (dual of [177186, 177069, 16]-code), using
(102, 117, large)-Net in Base 3 — Upper bound on s
There is no (102, 117, large)-net in base 3, because
- 13 times m-reduction [i] would yield (102, 104, large)-net in base 3, but