Best Known (119−11, 119, s)-Nets in Base 5
(119−11, 119, 3356071)-Net over F5 — Constructive and digital
Digital (108, 119, 3356071)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (12, 17, 631)-net over F5, using
- net defined by OOA [i] based on linear OOA(517, 631, F5, 6, 5) (dual of [(631, 6), 3769, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(517, 632, F5, 2, 5) (dual of [(632, 2), 1247, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(53, 31, F5, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
- appending kth column [i] based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- appending kth column [i] based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- linear OOA(514, 601, F5, 2, 5) (dual of [(601, 2), 1188, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(514, 1202, F5, 5) (dual of [1202, 1188, 6]-code), using
- trace code [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- OOA 2-folding [i] based on linear OA(514, 1202, F5, 5) (dual of [1202, 1188, 6]-code), using
- linear OOA(53, 31, F5, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(517, 632, F5, 2, 5) (dual of [(632, 2), 1247, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(517, 631, F5, 6, 5) (dual of [(631, 6), 3769, 6]-NRT-code), using
- digital (91, 102, 3355440)-net over F5, using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F25, using
- digital (12, 17, 631)-net over F5, using
(119−11, 119, large)-Net over F5 — Digital
Digital (108, 119, large)-net over F5, using
- 51 times duplication [i] based on digital (107, 118, large)-net over F5, using
- t-expansion [i] based on digital (104, 118, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5118, large, F5, 14) (dual of [large, large−118, 15]-code), using
- 7 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 7 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5118, large, F5, 14) (dual of [large, large−118, 15]-code), using
- t-expansion [i] based on digital (104, 118, large)-net over F5, using
(119−11, 119, large)-Net in Base 5 — Upper bound on s
There is no (108, 119, large)-net in base 5, because
- 9 times m-reduction [i] would yield (108, 110, large)-net in base 5, but