Best Known (144−23, 144, s)-Nets in Base 4
(144−23, 144, 5961)-Net over F4 — Constructive and digital
Digital (121, 144, 5961)-net over F4, using
- net defined by OOA [i] based on linear OOA(4144, 5961, F4, 23, 23) (dual of [(5961, 23), 136959, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4144, 65572, F4, 23) (dual of [65572, 65428, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4144, 65575, F4, 23) (dual of [65575, 65431, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4144, 65575, F4, 23) (dual of [65575, 65431, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4144, 65572, F4, 23) (dual of [65572, 65428, 24]-code), using
(144−23, 144, 36385)-Net over F4 — Digital
Digital (121, 144, 36385)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4144, 36385, F4, 23) (dual of [36385, 36241, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4144, 65575, F4, 23) (dual of [65575, 65431, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4144, 65575, F4, 23) (dual of [65575, 65431, 24]-code), using
(144−23, 144, large)-Net in Base 4 — Upper bound on s
There is no (121, 144, large)-net in base 4, because
- 21 times m-reduction [i] would yield (121, 123, large)-net in base 4, but