Best Known (149−22, 149, s)-Nets in Base 4
(149−22, 149, 23833)-Net over F4 — Constructive and digital
Digital (127, 149, 23833)-net over F4, using
- 41 times duplication [i] based on digital (126, 148, 23833)-net over F4, using
- net defined by OOA [i] based on linear OOA(4148, 23833, F4, 22, 22) (dual of [(23833, 22), 524178, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4148, 262163, F4, 22) (dual of [262163, 262015, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4148, 262165, F4, 22) (dual of [262165, 262017, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(4145, 262144, F4, 22) (dual of [262144, 261999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4148, 262165, F4, 22) (dual of [262165, 262017, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(4148, 262163, F4, 22) (dual of [262163, 262015, 23]-code), using
- net defined by OOA [i] based on linear OOA(4148, 23833, F4, 22, 22) (dual of [(23833, 22), 524178, 23]-NRT-code), using
(149−22, 149, 120250)-Net over F4 — Digital
Digital (127, 149, 120250)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4149, 120250, F4, 2, 22) (dual of [(120250, 2), 240351, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4149, 131083, F4, 2, 22) (dual of [(131083, 2), 262017, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4149, 262166, F4, 22) (dual of [262166, 262017, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4148, 262165, F4, 22) (dual of [262165, 262017, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(4145, 262144, F4, 22) (dual of [262144, 261999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4148, 262165, F4, 22) (dual of [262165, 262017, 23]-code), using
- OOA 2-folding [i] based on linear OA(4149, 262166, F4, 22) (dual of [262166, 262017, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(4149, 131083, F4, 2, 22) (dual of [(131083, 2), 262017, 23]-NRT-code), using
(149−22, 149, large)-Net in Base 4 — Upper bound on s
There is no (127, 149, large)-net in base 4, because
- 20 times m-reduction [i] would yield (127, 129, large)-net in base 4, but