Best Known (148, 171, s)-Nets in Base 4
(148, 171, 95325)-Net over F4 — Constructive and digital
Digital (148, 171, 95325)-net over F4, using
- net defined by OOA [i] based on linear OOA(4171, 95325, F4, 23, 23) (dual of [(95325, 23), 2192304, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using
(148, 171, 349528)-Net over F4 — Digital
Digital (148, 171, 349528)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4171, 349528, F4, 3, 23) (dual of [(349528, 3), 1048413, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4171, 1048584, F4, 23) (dual of [1048584, 1048413, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4171, 1048586, F4, 23) (dual of [1048586, 1048415, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(40, 10, F4, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4171, 1048586, F4, 23) (dual of [1048586, 1048415, 24]-code), using
- OOA 3-folding [i] based on linear OA(4171, 1048584, F4, 23) (dual of [1048584, 1048413, 24]-code), using
(148, 171, large)-Net in Base 4 — Upper bound on s
There is no (148, 171, large)-net in base 4, because
- 21 times m-reduction [i] would yield (148, 150, large)-net in base 4, but