Best Known (194, 233, s)-Nets in Base 4
(194, 233, 3449)-Net over F4 — Constructive and digital
Digital (194, 233, 3449)-net over F4, using
- net defined by OOA [i] based on linear OOA(4233, 3449, F4, 39, 39) (dual of [(3449, 39), 134278, 40]-NRT-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(4233, 65532, F4, 39) (dual of [65532, 65299, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(4233, 65536, F4, 39) (dual of [65536, 65303, 40]-code), using
- an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- discarding factors / shortening the dual code based on linear OA(4233, 65536, F4, 39) (dual of [65536, 65303, 40]-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(4233, 65532, F4, 39) (dual of [65532, 65299, 40]-code), using
(194, 233, 32772)-Net over F4 — Digital
Digital (194, 233, 32772)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4233, 32772, F4, 2, 39) (dual of [(32772, 2), 65311, 40]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4233, 65544, F4, 39) (dual of [65544, 65311, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- linear OA(4233, 65536, F4, 39) (dual of [65536, 65303, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(38) ⊂ Ce(37) [i] based on
- OOA 2-folding [i] based on linear OA(4233, 65544, F4, 39) (dual of [65544, 65311, 40]-code), using
(194, 233, large)-Net in Base 4 — Upper bound on s
There is no (194, 233, large)-net in base 4, because
- 37 times m-reduction [i] would yield (194, 196, large)-net in base 4, but