Best Known (124, 153, s)-Nets in Base 4
(124, 153, 1172)-Net over F4 — Constructive and digital
Digital (124, 153, 1172)-net over F4, using
- net defined by OOA [i] based on linear OOA(4153, 1172, F4, 29, 29) (dual of [(1172, 29), 33835, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4153, 16409, F4, 29) (dual of [16409, 16256, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 16410, F4, 29) (dual of [16410, 16257, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-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(28) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4153, 16410, F4, 29) (dual of [16410, 16257, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4153, 16409, F4, 29) (dual of [16409, 16256, 30]-code), using
(124, 153, 8905)-Net over F4 — Digital
Digital (124, 153, 8905)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4153, 8905, F4, 29) (dual of [8905, 8752, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 16410, F4, 29) (dual of [16410, 16257, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-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(28) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4153, 16410, F4, 29) (dual of [16410, 16257, 30]-code), using
(124, 153, 6934052)-Net in Base 4 — Upper bound on s
There is no (124, 153, 6934053)-net in base 4, because
- 1 times m-reduction [i] would yield (124, 152, 6934053)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 32 592614 595833 608585 849477 750046 241090 410174 107860 209659 933784 144849 340145 323031 953110 449456 > 4152 [i]