Best Known (140−16, 140, s)-Nets in Base 4
(140−16, 140, 524293)-Net over F4 — Constructive and digital
Digital (124, 140, 524293)-net over F4, using
- net defined by OOA [i] based on linear OOA(4140, 524293, F4, 16, 16) (dual of [(524293, 16), 8388548, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4140, 4194344, F4, 16) (dual of [4194344, 4194204, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4140, 4194348, F4, 16) (dual of [4194348, 4194208, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(4133, 4194305, F4, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(489, 4194305, F4, 11) (dual of [4194305, 4194216, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 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(4140, 4194348, F4, 16) (dual of [4194348, 4194208, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(4140, 4194344, F4, 16) (dual of [4194344, 4194204, 17]-code), using
(140−16, 140, 2097174)-Net over F4 — Digital
Digital (124, 140, 2097174)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4140, 2097174, F4, 2, 16) (dual of [(2097174, 2), 4194208, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4140, 4194348, F4, 16) (dual of [4194348, 4194208, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(4133, 4194305, F4, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(489, 4194305, F4, 11) (dual of [4194305, 4194216, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 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
- OOA 2-folding [i] based on linear OA(4140, 4194348, F4, 16) (dual of [4194348, 4194208, 17]-code), using
(140−16, 140, large)-Net in Base 4 — Upper bound on s
There is no (124, 140, large)-net in base 4, because
- 14 times m-reduction [i] would yield (124, 126, large)-net in base 4, but