Best Known (30, 30+11, s)-Nets in Base 9
(30, 30+11, 1315)-Net over F9 — Constructive and digital
Digital (30, 41, 1315)-net over F9, using
- net defined by OOA [i] based on linear OOA(941, 1315, F9, 11, 11) (dual of [(1315, 11), 14424, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(941, 6576, F9, 11) (dual of [6576, 6535, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(941, 6577, F9, 11) (dual of [6577, 6536, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(937, 6561, F9, 11) (dual of [6561, 6524, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(925, 6561, F9, 7) (dual of [6561, 6536, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(94, 16, F9, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,9)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(941, 6577, F9, 11) (dual of [6577, 6536, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(941, 6576, F9, 11) (dual of [6576, 6535, 12]-code), using
(30, 30+11, 6577)-Net over F9 — Digital
Digital (30, 41, 6577)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(941, 6577, F9, 11) (dual of [6577, 6536, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(937, 6561, F9, 11) (dual of [6561, 6524, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(925, 6561, F9, 7) (dual of [6561, 6536, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(94, 16, F9, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,9)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
(30, 30+11, large)-Net in Base 9 — Upper bound on s
There is no (30, 41, large)-net in base 9, because
- 9 times m-reduction [i] would yield (30, 32, large)-net in base 9, but