Best Known (145, 145+28, s)-Nets in Base 4
(145, 145+28, 4683)-Net over F4 — Constructive and digital
Digital (145, 173, 4683)-net over F4, using
- net defined by OOA [i] based on linear OOA(4173, 4683, F4, 28, 28) (dual of [(4683, 28), 130951, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4173, 65562, F4, 28) (dual of [65562, 65389, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4173, 65564, F4, 28) (dual of [65564, 65391, 29]-code), using
- 1 times truncation [i] based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-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
- 1 times truncation [i] based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4173, 65564, F4, 28) (dual of [65564, 65391, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(4173, 65562, F4, 28) (dual of [65562, 65389, 29]-code), using
(145, 145+28, 33788)-Net over F4 — Digital
Digital (145, 173, 33788)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4173, 33788, F4, 28) (dual of [33788, 33615, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4173, 65564, F4, 28) (dual of [65564, 65391, 29]-code), using
- 1 times truncation [i] based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-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
- 1 times truncation [i] based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4173, 65564, F4, 28) (dual of [65564, 65391, 29]-code), using
(145, 145+28, large)-Net in Base 4 — Upper bound on s
There is no (145, 173, large)-net in base 4, because
- 26 times m-reduction [i] would yield (145, 147, large)-net in base 4, but