Best Known (103, 119, s)-Nets in Base 3
(103, 119, 22148)-Net over F3 — Constructive and digital
Digital (103, 119, 22148)-net over F3, using
- net defined by OOA [i] based on linear OOA(3119, 22148, F3, 16, 16) (dual of [(22148, 16), 354249, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3119, 177184, F3, 16) (dual of [177184, 177065, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-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(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3119, 177184, F3, 16) (dual of [177184, 177065, 17]-code), using
(103, 119, 59062)-Net over F3 — Digital
Digital (103, 119, 59062)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3119, 59062, F3, 3, 16) (dual of [(59062, 3), 177067, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3119, 177186, F3, 16) (dual of [177186, 177067, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-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(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-code), using
- OOA 3-folding [i] based on linear OA(3119, 177186, F3, 16) (dual of [177186, 177067, 17]-code), using
(103, 119, large)-Net in Base 3 — Upper bound on s
There is no (103, 119, large)-net in base 3, because
- 14 times m-reduction [i] would yield (103, 105, large)-net in base 3, but