Best Known (156, 156+20, s)-Nets in Base 3
(156, 156+20, 159436)-Net over F3 — Constructive and digital
Digital (156, 176, 159436)-net over F3, using
- net defined by OOA [i] based on linear OOA(3176, 159436, F3, 20, 20) (dual of [(159436, 20), 3188544, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3176, 1594360, F3, 20) (dual of [1594360, 1594184, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3176, 1594368, F3, 20) (dual of [1594368, 1594192, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3176, 1594368, F3, 20) (dual of [1594368, 1594192, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3176, 1594360, F3, 20) (dual of [1594360, 1594184, 21]-code), using
(156, 156+20, 490195)-Net over F3 — Digital
Digital (156, 176, 490195)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3176, 490195, F3, 3, 20) (dual of [(490195, 3), 1470409, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3176, 531456, F3, 3, 20) (dual of [(531456, 3), 1594192, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3176, 1594368, F3, 20) (dual of [1594368, 1594192, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- OOA 3-folding [i] based on linear OA(3176, 1594368, F3, 20) (dual of [1594368, 1594192, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(3176, 531456, F3, 3, 20) (dual of [(531456, 3), 1594192, 21]-NRT-code), using
(156, 156+20, large)-Net in Base 3 — Upper bound on s
There is no (156, 176, large)-net in base 3, because
- 18 times m-reduction [i] would yield (156, 158, large)-net in base 3, but