Best Known (115, 130, s)-Nets in Base 3
(115, 130, 227760)-Net over F3 — Constructive and digital
Digital (115, 130, 227760)-net over F3, using
- net defined by OOA [i] based on linear OOA(3130, 227760, F3, 15, 15) (dual of [(227760, 15), 3416270, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3130, 1594321, F3, 15) (dual of [1594321, 1594191, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3130, 1594322, F3, 15) (dual of [1594322, 1594192, 16]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3130, 1594322, F3, 15) (dual of [1594322, 1594192, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3130, 1594321, F3, 15) (dual of [1594321, 1594191, 16]-code), using
(115, 130, 531440)-Net over F3 — Digital
Digital (115, 130, 531440)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3130, 531440, F3, 3, 15) (dual of [(531440, 3), 1594190, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3130, 1594320, F3, 15) (dual of [1594320, 1594190, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3130, 1594322, F3, 15) (dual of [1594322, 1594192, 16]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3130, 1594322, F3, 15) (dual of [1594322, 1594192, 16]-code), using
- OOA 3-folding [i] based on linear OA(3130, 1594320, F3, 15) (dual of [1594320, 1594190, 16]-code), using
(115, 130, large)-Net in Base 3 — Upper bound on s
There is no (115, 130, large)-net in base 3, because
- 13 times m-reduction [i] would yield (115, 117, large)-net in base 3, but