Best Known (133, 133+13, s)-Nets in Base 4
(133, 133+13, 2796200)-Net over F4 — Constructive and digital
Digital (133, 146, 2796200)-net over F4, using
- net defined by OOA [i] based on linear OOA(4146, 2796200, F4, 14, 13) (dual of [(2796200, 14), 39146654, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(4146, 8388601, F4, 2, 13) (dual of [(8388601, 2), 16777056, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4146, 8388602, F4, 2, 13) (dual of [(8388602, 2), 16777058, 14]-NRT-code), using
- trace code [i] based on linear OOA(1673, 4194301, F16, 2, 13) (dual of [(4194301, 2), 8388529, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1673, 8388602, F16, 13) (dual of [8388602, 8388529, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(1673, large, F16, 13) (dual of [large, large−73, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(1673, large, F16, 13) (dual of [large, large−73, 14]-code), using
- OOA 2-folding [i] based on linear OA(1673, 8388602, F16, 13) (dual of [8388602, 8388529, 14]-code), using
- trace code [i] based on linear OOA(1673, 4194301, F16, 2, 13) (dual of [(4194301, 2), 8388529, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4146, 8388602, F4, 2, 13) (dual of [(8388602, 2), 16777058, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(4146, 8388601, F4, 2, 13) (dual of [(8388601, 2), 16777056, 14]-NRT-code), using
(133, 133+13, large)-Net over F4 — Digital
Digital (133, 146, large)-net over F4, using
- 41 times duplication [i] based on digital (132, 145, large)-net over F4, using
- t-expansion [i] based on digital (130, 145, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
- t-expansion [i] based on digital (130, 145, large)-net over F4, using
(133, 133+13, large)-Net in Base 4 — Upper bound on s
There is no (133, 146, large)-net in base 4, because
- 11 times m-reduction [i] would yield (133, 135, large)-net in base 4, but