Best Known (100, 110, s)-Nets in Base 4
(100, 110, 3355440)-Net over F4 — Constructive and digital
Digital (100, 110, 3355440)-net over F4, using
- trace code for nets [i] based on digital (45, 55, 1677720)-net over F16, using
- net defined by OOA [i] based on linear OOA(1655, 1677720, F16, 10, 10) (dual of [(1677720, 10), 16777145, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(1655, 8388600, F16, 10) (dual of [8388600, 8388545, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1655, large, F16, 10) (dual of [large, large−55, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(1655, large, F16, 10) (dual of [large, large−55, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(1655, 8388600, F16, 10) (dual of [8388600, 8388545, 11]-code), using
- net defined by OOA [i] based on linear OOA(1655, 1677720, F16, 10, 10) (dual of [(1677720, 10), 16777145, 11]-NRT-code), using
(100, 110, large)-Net over F4 — Digital
Digital (100, 110, large)-net over F4, using
- 47 times duplication [i] based on digital (93, 103, large)-net over F4, using
- t-expansion [i] based on digital (92, 103, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4103, large, F4, 11) (dual of [large, large−103, 12]-code), using
- 6 times code embedding in larger space [i] based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 6 times code embedding in larger space [i] based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4103, large, F4, 11) (dual of [large, large−103, 12]-code), using
- t-expansion [i] based on digital (92, 103, large)-net over F4, using
(100, 110, large)-Net in Base 4 — Upper bound on s
There is no (100, 110, large)-net in base 4, because
- 8 times m-reduction [i] would yield (100, 102, large)-net in base 4, but