Best Known (235−25, 235, s)-Nets in Base 4
(235−25, 235, 699068)-Net over F4 — Constructive and digital
Digital (210, 235, 699068)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (6, 18, 18)-net 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
(235−25, 235, 4194321)-Net over F4 — Digital
Digital (210, 235, 4194321)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4235, 4194321, F4, 2, 25) (dual of [(4194321, 2), 8388407, 26]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(418, 20, F4, 2, 12) (dual of [(20, 2), 22, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,27P) [i] based on function field F/F4 with g(F) = 6 and N(F) ≥ 20, 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(418, 20, F4, 2, 12) (dual of [(20, 2), 22, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
(235−25, 235, large)-Net in Base 4 — Upper bound on s
There is no (210, 235, large)-net in base 4, because
- 23 times m-reduction [i] would yield (210, 212, large)-net in base 4, but