Best Known (100, 100+16, s)-Nets in Base 4
(100, 100+16, 32773)-Net over F4 — Constructive and digital
Digital (100, 116, 32773)-net over F4, using
- net defined by OOA [i] based on linear OOA(4116, 32773, F4, 16, 16) (dual of [(32773, 16), 524252, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4116, 262184, F4, 16) (dual of [262184, 262068, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4116, 262188, F4, 16) (dual of [262188, 262072, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(473, 262145, F4, 11) (dual of [262145, 262072, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, 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(4116, 262188, F4, 16) (dual of [262188, 262072, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(4116, 262184, F4, 16) (dual of [262184, 262068, 17]-code), using
(100, 100+16, 177747)-Net over F4 — Digital
Digital (100, 116, 177747)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4116, 177747, F4, 16) (dual of [177747, 177631, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4116, 262188, F4, 16) (dual of [262188, 262072, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(473, 262145, F4, 11) (dual of [262145, 262072, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, 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(4116, 262188, F4, 16) (dual of [262188, 262072, 17]-code), using
(100, 100+16, large)-Net in Base 4 — Upper bound on s
There is no (100, 116, large)-net in base 4, because
- 14 times m-reduction [i] would yield (100, 102, large)-net in base 4, but