Best Known (91, 103, s)-Nets in Base 4
(91, 103, 699055)-Net over F4 — Constructive and digital
Digital (91, 103, 699055)-net over F4, using
- net defined by OOA [i] based on linear OOA(4103, 699055, F4, 12, 12) (dual of [(699055, 12), 8388557, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4103, 4194330, F4, 12) (dual of [4194330, 4194227, 13]-code), using
- 2 times code embedding in larger space [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
- 2 times code embedding in larger space [i] based on linear OA(4101, 4194328, F4, 12) (dual of [4194328, 4194227, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(4103, 4194330, F4, 12) (dual of [4194330, 4194227, 13]-code), using
(91, 103, 2097165)-Net over F4 — Digital
Digital (91, 103, 2097165)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4103, 2097165, F4, 2, 12) (dual of [(2097165, 2), 4194227, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [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
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4101, 2097164, F4, 2, 12) (dual of [(2097164, 2), 4194227, 13]-NRT-code), using
(91, 103, large)-Net in Base 4 — Upper bound on s
There is no (91, 103, large)-net in base 4, because
- 10 times m-reduction [i] would yield (91, 93, large)-net in base 4, but