Best Known (134, 161, s)-Nets in Base 4
(134, 161, 5041)-Net over F4 — Constructive and digital
Digital (134, 161, 5041)-net over F4, using
- net defined by OOA [i] based on linear OOA(4161, 5041, F4, 27, 27) (dual of [(5041, 27), 135946, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4161, 65534, F4, 27) (dual of [65534, 65373, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4161, 65534, F4, 27) (dual of [65534, 65373, 28]-code), using
(134, 161, 31815)-Net over F4 — Digital
Digital (134, 161, 31815)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4161, 31815, F4, 2, 27) (dual of [(31815, 2), 63469, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4161, 32772, F4, 2, 27) (dual of [(32772, 2), 65383, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4161, 65544, F4, 27) (dual of [65544, 65383, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(4161, 65544, F4, 27) (dual of [65544, 65383, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(4161, 32772, F4, 2, 27) (dual of [(32772, 2), 65383, 28]-NRT-code), using
(134, 161, large)-Net in Base 4 — Upper bound on s
There is no (134, 161, large)-net in base 4, because
- 25 times m-reduction [i] would yield (134, 136, large)-net in base 4, but