Best Known (116, 148, s)-Nets in Base 9
(116, 148, 3692)-Net over F9 — Constructive and digital
Digital (116, 148, 3692)-net over F9, using
- 93 times duplication [i] based on digital (113, 145, 3692)-net over F9, using
- net defined by OOA [i] based on linear OOA(9145, 3692, F9, 32, 32) (dual of [(3692, 32), 117999, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(9145, 59072, F9, 32) (dual of [59072, 58927, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, 59073, F9, 32) (dual of [59073, 58928, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(9141, 59049, F9, 32) (dual of [59049, 58908, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(9145, 59073, F9, 32) (dual of [59073, 58928, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(9145, 59072, F9, 32) (dual of [59072, 58927, 33]-code), using
- net defined by OOA [i] based on linear OOA(9145, 3692, F9, 32, 32) (dual of [(3692, 32), 117999, 33]-NRT-code), using
(116, 148, 59081)-Net over F9 — Digital
Digital (116, 148, 59081)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9148, 59081, F9, 32) (dual of [59081, 58933, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- linear OA(9141, 59049, F9, 32) (dual of [59049, 58908, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(97, 32, F9, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
(116, 148, large)-Net in Base 9 — Upper bound on s
There is no (116, 148, large)-net in base 9, because
- 30 times m-reduction [i] would yield (116, 118, large)-net in base 9, but