Best Known (133, 133+16, s)-Nets in Base 3
(133, 133+16, 597876)-Net over F3 — Constructive and digital
Digital (133, 149, 597876)-net over F3, using
- net defined by OOA [i] based on linear OOA(3149, 597876, F3, 16, 16) (dual of [(597876, 16), 9565867, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3149, 4783008, F3, 16) (dual of [4783008, 4782859, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3149, 4783010, F3, 16) (dual of [4783010, 4782861, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, 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(3149, 4783010, F3, 16) (dual of [4783010, 4782861, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3149, 4783008, F3, 16) (dual of [4783008, 4782859, 17]-code), using
(133, 133+16, 1594336)-Net over F3 — Digital
Digital (133, 149, 1594336)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3149, 1594336, F3, 3, 16) (dual of [(1594336, 3), 4782859, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3149, 4783008, F3, 16) (dual of [4783008, 4782859, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3149, 4783010, F3, 16) (dual of [4783010, 4782861, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, 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(3149, 4783010, F3, 16) (dual of [4783010, 4782861, 17]-code), using
- OOA 3-folding [i] based on linear OA(3149, 4783008, F3, 16) (dual of [4783008, 4782859, 17]-code), using
(133, 133+16, large)-Net in Base 3 — Upper bound on s
There is no (133, 149, large)-net in base 3, because
- 14 times m-reduction [i] would yield (133, 135, large)-net in base 3, but