Best Known (92, 92+14, s)-Nets in Base 4
(92, 92+14, 149801)-Net over F4 — Constructive and digital
Digital (92, 106, 149801)-net over F4, using
- net defined by OOA [i] based on linear OOA(4106, 149801, F4, 14, 14) (dual of [(149801, 14), 2097108, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4106, 1048607, F4, 14) (dual of [1048607, 1048501, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4106, 1048611, F4, 14) (dual of [1048611, 1048505, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(471, 1048576, F4, 10) (dual of [1048576, 1048505, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-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(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(4106, 1048611, F4, 14) (dual of [1048611, 1048505, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(4106, 1048607, F4, 14) (dual of [1048607, 1048501, 15]-code), using
(92, 92+14, 524305)-Net over F4 — Digital
Digital (92, 106, 524305)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4106, 524305, F4, 2, 14) (dual of [(524305, 2), 1048504, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4106, 1048610, F4, 14) (dual of [1048610, 1048504, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4106, 1048611, F4, 14) (dual of [1048611, 1048505, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(471, 1048576, F4, 10) (dual of [1048576, 1048505, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-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(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(4106, 1048611, F4, 14) (dual of [1048611, 1048505, 15]-code), using
- OOA 2-folding [i] based on linear OA(4106, 1048610, F4, 14) (dual of [1048610, 1048504, 15]-code), using
(92, 92+14, large)-Net in Base 4 — Upper bound on s
There is no (92, 106, large)-net in base 4, because
- 12 times m-reduction [i] would yield (92, 94, large)-net in base 4, but