Best Known (97, 109, s)-Nets in Base 4
(97, 109, 1398100)-Net over F4 — Constructive and digital
Digital (97, 109, 1398100)-net over F4, using
- t-expansion [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, 109, 4798465)-Net over F4 — Digital
Digital (97, 109, 4798465)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4109, 4798465, F4, 12) (dual of [4798465, 4798356, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 12) (dual of [large, large−109, 13]-code), using
- strength reduction [i] 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]
- strength reduction [i] based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 12) (dual of [large, large−109, 13]-code), using
(97, 109, large)-Net in Base 4 — Upper bound on s
There is no (97, 109, large)-net in base 4, because
- 10 times m-reduction [i] would yield (97, 99, large)-net in base 4, but