Best Known (131−16, 131, s)-Nets in Base 3
(131−16, 131, 199290)-Net over F3 — Constructive and digital
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
(131−16, 131, 398580)-Net over F3 — Digital
Digital (115, 131, 398580)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3131, 398580, F3, 4, 16) (dual of [(398580, 4), 1594189, 17]-NRT-code), using
- OOA 4-folding [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
- OOA 4-folding [i] based on linear OA(3131, 1594320, F3, 16) (dual of [1594320, 1594189, 17]-code), using
(131−16, 131, large)-Net in Base 3 — Upper bound on s
There is no (115, 131, large)-net in base 3, because
- 14 times m-reduction [i] would yield (115, 117, large)-net in base 3, but