Best Known (89, 101, s)-Nets in Base 4
(89, 101, 699054)-Net over F4 — Constructive and digital
Digital (89, 101, 699054)-net over F4, using
- net defined by OOA [i] based on linear OOA(4101, 699054, F4, 12, 12) (dual of [(699054, 12), 8388547, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4101, 4194324, F4, 12) (dual of [4194324, 4194223, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 4194327, F4, 12) (dual of [4194327, 4194226, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(41, 23, F4, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(4101, 4194327, F4, 12) (dual of [4194327, 4194226, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(4101, 4194324, F4, 12) (dual of [4194324, 4194223, 13]-code), using
(89, 101, 2097164)-Net over F4 — Digital
Digital (89, 101, 2097164)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4101, 2097164, F4, 2, 12) (dual of [(2097164, 2), 4194227, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4101, 4194328, F4, 12) (dual of [4194328, 4194227, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(4101, 4194328, F4, 12) (dual of [4194328, 4194227, 13]-code), using
(89, 101, large)-Net in Base 4 — Upper bound on s
There is no (89, 101, large)-net in base 4, because
- 10 times m-reduction [i] would yield (89, 91, large)-net in base 4, but