Best Known (124, 140, s)-Nets in Base 3
(124, 140, 199297)-Net over F3 — Constructive and digital
Digital (124, 140, 199297)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (115, 131, 199290)-net over F3, using
- net defined by OOA [i] based on linear OOA(3131, 199290, F3, 16, 16) (dual of [(199290, 16), 3188509, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3131, 1594320, F3, 16) (dual of [1594320, 1594189, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3131, 1594320, F3, 16) (dual of [1594320, 1594189, 17]-code), using
- net defined by OOA [i] based on linear OOA(3131, 199290, F3, 16, 16) (dual of [(199290, 16), 3188509, 17]-NRT-code), using
- digital (1, 9, 7)-net over F3, using
(124, 140, 531457)-Net over F3 — Digital
Digital (124, 140, 531457)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3140, 531457, F3, 3, 16) (dual of [(531457, 3), 1594231, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3140, 1594371, F3, 16) (dual of [1594371, 1594231, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(39, 48, F3, 4) (dual of [48, 39, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- OOA 3-folding [i] based on linear OA(3140, 1594371, F3, 16) (dual of [1594371, 1594231, 17]-code), using
(124, 140, large)-Net in Base 3 — Upper bound on s
There is no (124, 140, large)-net in base 3, because
- 14 times m-reduction [i] would yield (124, 126, large)-net in base 3, but