Best Known (207, 232, s)-Nets in Base 4
(207, 232, 699064)-Net over F4 — Constructive and digital
Digital (207, 232, 699064)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (192, 217, 699050)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 699050, F4, 25, 25) (dual of [(699050, 25), 17476033, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4217, 8388601, F4, 25) (dual of [8388601, 8388384, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4217, 8388601, F4, 25) (dual of [8388601, 8388384, 26]-code), using
- net defined by OOA [i] based on linear OOA(4217, 699050, F4, 25, 25) (dual of [(699050, 25), 17476033, 26]-NRT-code), using
- digital (3, 15, 14)-net over F4, using
(207, 232, 4194315)-Net over F4 — Digital
Digital (207, 232, 4194315)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4232, 4194315, F4, 2, 25) (dual of [(4194315, 2), 8388398, 26]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(415, 14, F4, 2, 12) (dual of [(14, 2), 13, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,15P) [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- linear OOA(4217, 4194301, F4, 2, 25) (dual of [(4194301, 2), 8388385, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-code), using
- linear OOA(415, 14, F4, 2, 12) (dual of [(14, 2), 13, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
(207, 232, large)-Net in Base 4 — Upper bound on s
There is no (207, 232, large)-net in base 4, because
- 23 times m-reduction [i] would yield (207, 209, large)-net in base 4, but