Best Known (149−25, 149, s)-Nets in Base 4
(149−25, 149, 5463)-Net over F4 — Constructive and digital
Digital (124, 149, 5463)-net over F4, using
- net defined by OOA [i] based on linear OOA(4149, 5463, F4, 25, 25) (dual of [(5463, 25), 136426, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4149, 65557, F4, 25) (dual of [65557, 65408, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- 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(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(43, 20, F4, 2) (dual of [20, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(4149, 65557, F4, 25) (dual of [65557, 65408, 26]-code), using
(149−25, 149, 31794)-Net over F4 — Digital
Digital (124, 149, 31794)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4149, 31794, F4, 2, 25) (dual of [(31794, 2), 63439, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4149, 32778, F4, 2, 25) (dual of [(32778, 2), 65407, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4149, 65556, F4, 25) (dual of [65556, 65407, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4149, 65557, F4, 25) (dual of [65557, 65408, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- 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(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(43, 20, F4, 2) (dual of [20, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4149, 65557, F4, 25) (dual of [65557, 65408, 26]-code), using
- OOA 2-folding [i] based on linear OA(4149, 65556, F4, 25) (dual of [65556, 65407, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(4149, 32778, F4, 2, 25) (dual of [(32778, 2), 65407, 26]-NRT-code), using
(149−25, 149, large)-Net in Base 4 — Upper bound on s
There is no (124, 149, large)-net in base 4, because
- 23 times m-reduction [i] would yield (124, 126, large)-net in base 4, but