Best Known (103−12, 103, s)-Nets in Base 5
(103−12, 103, 1398152)-Net over F5 — Constructive and digital
Digital (91, 103, 1398152)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (6, 12, 52)-net over F5, using
- trace code for nets [i] based on digital (0, 6, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- trace code for nets [i] based on digital (0, 6, 26)-net over F25, using
- digital (79, 91, 1398100)-net over F5, using
- net defined by OOA [i] based on linear OOA(591, 1398100, F5, 12, 12) (dual of [(1398100, 12), 16777109, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(591, 8388600, F5, 12) (dual of [8388600, 8388509, 13]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(591, 8388600, F5, 12) (dual of [8388600, 8388509, 13]-code), using
- net defined by OOA [i] based on linear OOA(591, 1398100, F5, 12, 12) (dual of [(1398100, 12), 16777109, 13]-NRT-code), using
- digital (6, 12, 52)-net over F5, using
(103−12, 103, large)-Net over F5 — Digital
Digital (91, 103, large)-net over F5, using
- 53 times duplication [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
(103−12, 103, large)-Net in Base 5 — Upper bound on s
There is no (91, 103, large)-net in base 5, because
- 10 times m-reduction [i] would yield (91, 93, large)-net in base 5, but