Best Known (97, 110, s)-Nets in Base 4
(97, 110, 1398100)-Net over F4 — Constructive and digital
Digital (97, 110, 1398100)-net over F4, using
- 41 times duplication [i] based on digital (96, 109, 1398100)-net over F4, using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
(97, 110, 4194301)-Net over F4 — Digital
Digital (97, 110, 4194301)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4110, 4194301, F4, 2, 13) (dual of [(4194301, 2), 8388492, 14]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4109, 4194301, F4, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-code), using
- 41 times duplication [i] based on linear OOA(4109, 4194301, F4, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
(97, 110, large)-Net in Base 4 — Upper bound on s
There is no (97, 110, large)-net in base 4, because
- 11 times m-reduction [i] would yield (97, 99, large)-net in base 4, but