Best Known (158, 158+24, s)-Nets in Base 4
(158, 158+24, 87383)-Net over F4 — Constructive and digital
Digital (158, 182, 87383)-net over F4, using
- net defined by OOA [i] based on linear OOA(4182, 87383, F4, 24, 24) (dual of [(87383, 24), 2097010, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4182, 1048596, F4, 24) (dual of [1048596, 1048414, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4182, 1048597, F4, 24) (dual of [1048597, 1048415, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(41, 21, F4, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4182, 1048597, F4, 24) (dual of [1048597, 1048415, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4182, 1048596, F4, 24) (dual of [1048596, 1048414, 25]-code), using
(158, 158+24, 418667)-Net over F4 — Digital
Digital (158, 182, 418667)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4182, 418667, F4, 2, 24) (dual of [(418667, 2), 837152, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 524298, F4, 2, 24) (dual of [(524298, 2), 1048414, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4182, 1048596, F4, 24) (dual of [1048596, 1048414, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4182, 1048597, F4, 24) (dual of [1048597, 1048415, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(41, 21, F4, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4182, 1048597, F4, 24) (dual of [1048597, 1048415, 25]-code), using
- OOA 2-folding [i] based on linear OA(4182, 1048596, F4, 24) (dual of [1048596, 1048414, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 524298, F4, 2, 24) (dual of [(524298, 2), 1048414, 25]-NRT-code), using
(158, 158+24, large)-Net in Base 4 — Upper bound on s
There is no (158, 182, large)-net in base 4, because
- 22 times m-reduction [i] would yield (158, 160, large)-net in base 4, but