Best Known (97−11, 97, s)-Nets in Base 4
(97−11, 97, 1677720)-Net over F4 — Constructive and digital
Digital (86, 97, 1677720)-net over F4, using
- net defined by OOA [i] based on linear OOA(497, 1677720, F4, 11, 11) (dual of [(1677720, 11), 18454823, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(497, 8388601, F4, 11) (dual of [8388601, 8388504, 12]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(497, 8388601, F4, 11) (dual of [8388601, 8388504, 12]-code), using
(97−11, 97, 4194301)-Net over F4 — Digital
Digital (86, 97, 4194301)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(497, 4194301, F4, 2, 11) (dual of [(4194301, 2), 8388505, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(497, 8388602, F4, 11) (dual of [8388602, 8388505, 12]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- OOA 2-folding [i] based on linear OA(497, 8388602, F4, 11) (dual of [8388602, 8388505, 12]-code), using
(97−11, 97, large)-Net in Base 4 — Upper bound on s
There is no (86, 97, large)-net in base 4, because
- 9 times m-reduction [i] would yield (86, 88, large)-net in base 4, but