Best Known (83, 94, s)-Nets in Base 4
(83, 94, 838868)-Net over F4 — Constructive and digital
Digital (83, 94, 838868)-net over F4, using
- net defined by OOA [i] based on linear OOA(494, 838868, F4, 11, 11) (dual of [(838868, 11), 9227454, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(494, 4194341, F4, 11) (dual of [4194341, 4194247, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(494, 4194342, F4, 11) (dual of [4194342, 4194248, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(489, 4194304, F4, 11) (dual of [4194304, 4194215, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(456, 4194304, F4, 7) (dual of [4194304, 4194248, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-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(10) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(494, 4194342, F4, 11) (dual of [4194342, 4194248, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(494, 4194341, F4, 11) (dual of [4194341, 4194247, 12]-code), using
(83, 94, 2300994)-Net over F4 — Digital
Digital (83, 94, 2300994)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(494, 2300994, F4, 11) (dual of [2300994, 2300900, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(494, 4194342, F4, 11) (dual of [4194342, 4194248, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(489, 4194304, F4, 11) (dual of [4194304, 4194215, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(456, 4194304, F4, 7) (dual of [4194304, 4194248, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-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(10) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(494, 4194342, F4, 11) (dual of [4194342, 4194248, 12]-code), using
(83, 94, large)-Net in Base 4 — Upper bound on s
There is no (83, 94, large)-net in base 4, because
- 9 times m-reduction [i] would yield (83, 85, large)-net in base 4, but