Best Known (114−14, 114, s)-Nets in Base 5
(114−14, 114, 1198371)-Net over F5 — Constructive and digital
Digital (100, 114, 1198371)-net over F5, using
- 53 times duplication [i] based on digital (97, 111, 1198371)-net over F5, using
- net defined by OOA [i] based on linear OOA(5111, 1198371, F5, 14, 14) (dual of [(1198371, 14), 16777083, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(5111, 8388597, F5, 14) (dual of [8388597, 8388486, 15]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(5111, 8388597, F5, 14) (dual of [8388597, 8388486, 15]-code), using
- net defined by OOA [i] based on linear OOA(5111, 1198371, F5, 14, 14) (dual of [(1198371, 14), 16777083, 15]-NRT-code), using
(114−14, 114, 5049731)-Net over F5 — Digital
Digital (100, 114, 5049731)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5114, 5049731, F5, 14) (dual of [5049731, 5049617, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5114, large, F5, 14) (dual of [large, large−114, 15]-code), using
- 3 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]
- 3 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5114, large, F5, 14) (dual of [large, large−114, 15]-code), using
(114−14, 114, large)-Net in Base 5 — Upper bound on s
There is no (100, 114, large)-net in base 5, because
- 12 times m-reduction [i] would yield (100, 102, large)-net in base 5, but