Best Known (240−32, 240, s)-Nets in Base 4
(240−32, 240, 65536)-Net over F4 — Constructive and digital
Digital (208, 240, 65536)-net over F4, using
- net defined by OOA [i] based on linear OOA(4240, 65536, F4, 32, 32) (dual of [(65536, 32), 2096912, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(4240, 1048576, F4, 32) (dual of [1048576, 1048336, 33]-code), using
- 1 times truncation [i] based on linear OA(4241, 1048577, F4, 33) (dual of [1048577, 1048336, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4241, 1048577, F4, 33) (dual of [1048577, 1048336, 34]-code), using
- OA 16-folding and stacking [i] based on linear OA(4240, 1048576, F4, 32) (dual of [1048576, 1048336, 33]-code), using
(240−32, 240, 349525)-Net over F4 — Digital
Digital (208, 240, 349525)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4240, 349525, F4, 3, 32) (dual of [(349525, 3), 1048335, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4240, 1048575, F4, 32) (dual of [1048575, 1048335, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(4240, 1048576, F4, 32) (dual of [1048576, 1048336, 33]-code), using
- 1 times truncation [i] based on linear OA(4241, 1048577, F4, 33) (dual of [1048577, 1048336, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4241, 1048577, F4, 33) (dual of [1048577, 1048336, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4240, 1048576, F4, 32) (dual of [1048576, 1048336, 33]-code), using
- OOA 3-folding [i] based on linear OA(4240, 1048575, F4, 32) (dual of [1048575, 1048335, 33]-code), using
(240−32, 240, large)-Net in Base 4 — Upper bound on s
There is no (208, 240, large)-net in base 4, because
- 30 times m-reduction [i] would yield (208, 210, large)-net in base 4, but