Best Known (35, 41, s)-Nets in Base 4
(35, 41, 349528)-Net over F4 — Constructive and digital
Digital (35, 41, 349528)-net over F4, using
- net defined by OOA [i] based on linear OOA(441, 349528, F4, 6, 6) (dual of [(349528, 6), 2097127, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(441, 1048584, F4, 6) (dual of [1048584, 1048543, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(441, 1048586, F4, 6) (dual of [1048586, 1048545, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 10, F4, 0) (dual of [10, 10, 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(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(441, 1048586, F4, 6) (dual of [1048586, 1048545, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(441, 1048584, F4, 6) (dual of [1048584, 1048543, 7]-code), using
(35, 41, 773624)-Net over F4 — Digital
Digital (35, 41, 773624)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(441, 773624, F4, 6) (dual of [773624, 773583, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using
(35, 41, large)-Net in Base 4 — Upper bound on s
There is no (35, 41, large)-net in base 4, because
- 4 times m-reduction [i] would yield (35, 37, large)-net in base 4, but