Best Known (104, 104+15, s)-Nets in Base 3
(104, 104+15, 25315)-Net over F3 — Constructive and digital
Digital (104, 119, 25315)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 9)-net over F3, using
- digital (95, 110, 25306)-net over F3, using
- net defined by OOA [i] based on linear OOA(3110, 25306, F3, 15, 15) (dual of [(25306, 15), 379480, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3110, 177143, F3, 15) (dual of [177143, 177033, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3110, 177146, F3, 15) (dual of [177146, 177036, 16]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3110, 177146, F3, 15) (dual of [177146, 177036, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3110, 177143, F3, 15) (dual of [177143, 177033, 16]-code), using
- net defined by OOA [i] based on linear OOA(3110, 25306, F3, 15, 15) (dual of [(25306, 15), 379480, 16]-NRT-code), using
(104, 104+15, 88594)-Net over F3 — Digital
Digital (104, 119, 88594)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3119, 88594, F3, 2, 15) (dual of [(88594, 2), 177069, 16]-NRT-code), using
- strength reduction [i] based on linear OOA(3119, 88594, F3, 2, 16) (dual of [(88594, 2), 177069, 17]-NRT-code), using
- OOA 2-folding [i] 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
- OOA 2-folding [i] based on linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-code), using
- strength reduction [i] based on linear OOA(3119, 88594, F3, 2, 16) (dual of [(88594, 2), 177069, 17]-NRT-code), using
(104, 104+15, large)-Net in Base 3 — Upper bound on s
There is no (104, 119, large)-net in base 3, because
- 13 times m-reduction [i] would yield (104, 106, large)-net in base 3, but