Best Known (100−11, 100, s)-Nets in Base 5
(100−11, 100, 1678921)-Net over F5 — Constructive and digital
Digital (89, 100, 1678921)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (14, 19, 1201)-net over F5, using
- net defined by OOA [i] based on linear OOA(519, 1201, F5, 6, 5) (dual of [(1201, 6), 7187, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(519, 1202, F5, 2, 5) (dual of [(1202, 2), 2385, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(55, 781, F5, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
- appending kth column [i] based on linear OA(55, 781, F5, 2) (dual of [781, 776, 3]-code), using
- Hamming code H(5,5) [i]
- appending kth column [i] based on linear OA(55, 781, F5, 2) (dual of [781, 776, 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(55, 781, F5, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(519, 1202, F5, 2, 5) (dual of [(1202, 2), 2385, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(519, 1201, F5, 6, 5) (dual of [(1201, 6), 7187, 6]-NRT-code), using
- digital (70, 81, 1677720)-net over F5, using
- net defined by OOA [i] based on linear OOA(581, 1677720, F5, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(581, 8388601, F5, 11) (dual of [8388601, 8388520, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, 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(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(581, 8388601, F5, 11) (dual of [8388601, 8388520, 12]-code), using
- net defined by OOA [i] based on linear OOA(581, 1677720, F5, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
- digital (14, 19, 1201)-net over F5, using
(100−11, 100, large)-Net over F5 — Digital
Digital (89, 100, large)-net over F5, using
- t-expansion [i] based on digital (88, 100, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5100, large, F5, 12) (dual of [large, large−100, 13]-code), using
- 9 times code embedding in larger space [i] based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 9 times code embedding in larger space [i] based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5100, large, F5, 12) (dual of [large, large−100, 13]-code), using
(100−11, 100, large)-Net in Base 5 — Upper bound on s
There is no (89, 100, large)-net in base 5, because
- 9 times m-reduction [i] would yield (89, 91, large)-net in base 5, but