Best Known (194, 194+36, s)-Nets in Base 4
(194, 194+36, 3644)-Net over F4 — Constructive and digital
Digital (194, 230, 3644)-net over F4, using
- net defined by OOA [i] based on linear OOA(4230, 3644, F4, 36, 36) (dual of [(3644, 36), 130954, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(4230, 65592, F4, 36) (dual of [65592, 65362, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4230, 65597, F4, 36) (dual of [65597, 65367, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 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(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4230, 65597, F4, 36) (dual of [65597, 65367, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(4230, 65592, F4, 36) (dual of [65592, 65362, 37]-code), using
(194, 194+36, 51189)-Net over F4 — Digital
Digital (194, 230, 51189)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4230, 51189, F4, 36) (dual of [51189, 50959, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4230, 65597, F4, 36) (dual of [65597, 65367, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 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(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4230, 65597, F4, 36) (dual of [65597, 65367, 37]-code), using
(194, 194+36, large)-Net in Base 4 — Upper bound on s
There is no (194, 230, large)-net in base 4, because
- 34 times m-reduction [i] would yield (194, 196, large)-net in base 4, but