Best Known (120, 120+23, s)-Nets in Base 4
(120, 120+23, 5960)-Net over F4 — Constructive and digital
Digital (120, 143, 5960)-net over F4, using
- 41 times duplication [i] based on digital (119, 142, 5960)-net over F4, using
- net defined by OOA [i] based on linear OOA(4142, 5960, F4, 23, 23) (dual of [(5960, 23), 136938, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4142, 65561, F4, 23) (dual of [65561, 65419, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4142, 65565, F4, 23) (dual of [65565, 65423, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [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(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4142, 65565, F4, 23) (dual of [65565, 65423, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4142, 65561, F4, 23) (dual of [65561, 65419, 24]-code), using
- net defined by OOA [i] based on linear OOA(4142, 5960, F4, 23, 23) (dual of [(5960, 23), 136938, 24]-NRT-code), using
(120, 120+23, 34059)-Net over F4 — Digital
Digital (120, 143, 34059)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4143, 34059, F4, 23) (dual of [34059, 33916, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4143, 65567, F4, 23) (dual of [65567, 65424, 24]-code), using
- construction XX applied to Ce(22) ⊂ Ce(18) ⊂ 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(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(22) ⊂ Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4143, 65567, F4, 23) (dual of [65567, 65424, 24]-code), using
(120, 120+23, large)-Net in Base 4 — Upper bound on s
There is no (120, 143, large)-net in base 4, because
- 21 times m-reduction [i] would yield (120, 122, large)-net in base 4, but