Best Known (102, 102+25, s)-Nets in Base 4
(102, 102+25, 1365)-Net over F4 — Constructive and digital
Digital (102, 127, 1365)-net over F4, using
- net defined by OOA [i] based on linear OOA(4127, 1365, F4, 25, 25) (dual of [(1365, 25), 33998, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4127, 16381, F4, 25) (dual of [16381, 16254, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4127, 16381, F4, 25) (dual of [16381, 16254, 26]-code), using
(102, 102+25, 7936)-Net over F4 — Digital
Digital (102, 127, 7936)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4127, 7936, F4, 2, 25) (dual of [(7936, 2), 15745, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4127, 8192, F4, 2, 25) (dual of [(8192, 2), 16257, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- OOA 2-folding [i] based on linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(4127, 8192, F4, 2, 25) (dual of [(8192, 2), 16257, 26]-NRT-code), using
(102, 102+25, 3697166)-Net in Base 4 — Upper bound on s
There is no (102, 127, 3697167)-net in base 4, because
- 1 times m-reduction [i] would yield (102, 126, 3697167)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7237 028775 676985 181672 985334 339390 079761 197604 567488 780526 016319 764241 918795 > 4126 [i]