Best Known (148−29, 148, s)-Nets in Base 4
(148−29, 148, 1170)-Net over F4 — Constructive and digital
Digital (119, 148, 1170)-net over F4, using
- net defined by OOA [i] based on linear OOA(4148, 1170, F4, 29, 29) (dual of [(1170, 29), 33782, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4148, 16381, F4, 29) (dual of [16381, 16233, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4148, 16381, F4, 29) (dual of [16381, 16233, 30]-code), using
(148−29, 148, 8192)-Net over F4 — Digital
Digital (119, 148, 8192)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4148, 8192, F4, 2, 29) (dual of [(8192, 2), 16236, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- OOA 2-folding [i] based on linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using
(148−29, 148, 4226347)-Net in Base 4 — Upper bound on s
There is no (119, 148, 4226348)-net in base 4, because
- 1 times m-reduction [i] would yield (119, 147, 4226348)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 31828 695407 312921 127513 497972 147814 929418 954238 447156 421193 722543 616377 424514 352709 373096 > 4147 [i]