Best Known (100−21, 100, s)-Nets in Base 9
(100−21, 100, 5908)-Net over F9 — Constructive and digital
Digital (79, 100, 5908)-net over F9, using
- 92 times duplication [i] based on digital (77, 98, 5908)-net over F9, using
- net defined by OOA [i] based on linear OOA(998, 5908, F9, 21, 21) (dual of [(5908, 21), 123970, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(998, 59081, F9, 21) (dual of [59081, 58983, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(991, 59049, F9, 21) (dual of [59049, 58958, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(966, 59049, F9, 15) (dual of [59049, 58983, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(20) ⊂ Ce(14) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(998, 59081, F9, 21) (dual of [59081, 58983, 22]-code), using
- net defined by OOA [i] based on linear OOA(998, 5908, F9, 21, 21) (dual of [(5908, 21), 123970, 22]-NRT-code), using
(100−21, 100, 61305)-Net over F9 — Digital
Digital (79, 100, 61305)-net over F9, using
(100−21, 100, large)-Net in Base 9 — Upper bound on s
There is no (79, 100, large)-net in base 9, because
- 19 times m-reduction [i] would yield (79, 81, large)-net in base 9, but