Best Known (113, 132, s)-Nets in Base 4
(113, 132, 29130)-Net over F4 — Constructive and digital
Digital (113, 132, 29130)-net over F4, using
- net defined by OOA [i] based on linear OOA(4132, 29130, F4, 19, 19) (dual of [(29130, 19), 553338, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4132, 262171, F4, 19) (dual of [262171, 262039, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4132, 262176, F4, 19) (dual of [262176, 262044, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(4127, 262144, F4, 19) (dual of [262144, 262017, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4100, 262144, F4, 15) (dual of [262144, 262044, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4132, 262176, F4, 19) (dual of [262176, 262044, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4132, 262171, F4, 19) (dual of [262171, 262039, 20]-code), using
(113, 132, 131088)-Net over F4 — Digital
Digital (113, 132, 131088)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4132, 131088, F4, 2, 19) (dual of [(131088, 2), 262044, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4132, 262176, F4, 19) (dual of [262176, 262044, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(4127, 262144, F4, 19) (dual of [262144, 262017, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4100, 262144, F4, 15) (dual of [262144, 262044, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- OOA 2-folding [i] based on linear OA(4132, 262176, F4, 19) (dual of [262176, 262044, 20]-code), using
(113, 132, large)-Net in Base 4 — Upper bound on s
There is no (113, 132, large)-net in base 4, because
- 17 times m-reduction [i] would yield (113, 115, large)-net in base 4, but