Best Known (141−16, 141, s)-Nets in Base 3
(141−16, 141, 597871)-Net over F3 — Constructive and digital
Digital (125, 141, 597871)-net over F3, using
- net defined by OOA [i] based on linear OOA(3141, 597871, F3, 16, 16) (dual of [(597871, 16), 9565795, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3141, 4782968, F3, 16) (dual of [4782968, 4782827, 17]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3141, 4782968, F3, 16) (dual of [4782968, 4782827, 17]-code), using
(141−16, 141, 1195742)-Net over F3 — Digital
Digital (125, 141, 1195742)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3141, 1195742, F3, 4, 16) (dual of [(1195742, 4), 4782827, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3141, 4782968, F3, 16) (dual of [4782968, 4782827, 17]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using
- OOA 4-folding [i] based on linear OA(3141, 4782968, F3, 16) (dual of [4782968, 4782827, 17]-code), using
(141−16, 141, large)-Net in Base 3 — Upper bound on s
There is no (125, 141, large)-net in base 3, because
- 14 times m-reduction [i] would yield (125, 127, large)-net in base 3, but