Best Known (98−15, 98, s)-Nets in Base 9
(98−15, 98, 683287)-Net over F9 — Constructive and digital
Digital (83, 98, 683287)-net over F9, using
- net defined by OOA [i] based on linear OOA(998, 683287, F9, 15, 15) (dual of [(683287, 15), 10249207, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(998, 4783010, F9, 15) (dual of [4783010, 4782912, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(96, 41, F9, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(998, 4783010, F9, 15) (dual of [4783010, 4782912, 16]-code), using
(98−15, 98, 4783010)-Net over F9 — Digital
Digital (83, 98, 4783010)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(998, 4783010, F9, 15) (dual of [4783010, 4782912, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(96, 41, F9, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
(98−15, 98, large)-Net in Base 9 — Upper bound on s
There is no (83, 98, large)-net in base 9, because
- 13 times m-reduction [i] would yield (83, 85, large)-net in base 9, but