Best Known (88, 88+16, s)-Nets in Base 4
(88, 88+16, 8197)-Net over F4 — Constructive and digital
Digital (88, 104, 8197)-net over F4, using
- net defined by OOA [i] based on linear OOA(4104, 8197, F4, 16, 16) (dual of [(8197, 16), 131048, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4104, 65576, F4, 16) (dual of [65576, 65472, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(465, 65537, F4, 11) (dual of [65537, 65472, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [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 C([0,8]) ⊂ C([0,5]) [i] based on
- OA 8-folding and stacking [i] based on linear OA(4104, 65576, F4, 16) (dual of [65576, 65472, 17]-code), using
(88, 88+16, 54162)-Net over F4 — Digital
Digital (88, 104, 54162)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4104, 54162, F4, 16) (dual of [54162, 54058, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4104, 65576, F4, 16) (dual of [65576, 65472, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(465, 65537, F4, 11) (dual of [65537, 65472, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [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 C([0,8]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4104, 65576, F4, 16) (dual of [65576, 65472, 17]-code), using
(88, 88+16, large)-Net in Base 4 — Upper bound on s
There is no (88, 104, large)-net in base 4, because
- 14 times m-reduction [i] would yield (88, 90, large)-net in base 4, but