Best Known (61, 61+16, s)-Nets in Base 9
(61, 61+16, 7385)-Net over F9 — Constructive and digital
Digital (61, 77, 7385)-net over F9, using
- net defined by OOA [i] based on linear OOA(977, 7385, F9, 16, 16) (dual of [(7385, 16), 118083, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(977, 59080, F9, 16) (dual of [59080, 59003, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(971, 59049, F9, 16) (dual of [59049, 58978, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(946, 59049, F9, 11) (dual of [59049, 59003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(96, 31, F9, 4) (dual of [31, 25, 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(15) ⊂ Ce(10) [i] based on
- OA 8-folding and stacking [i] based on linear OA(977, 59080, F9, 16) (dual of [59080, 59003, 17]-code), using
(61, 61+16, 63558)-Net over F9 — Digital
Digital (61, 77, 63558)-net over F9, using
(61, 61+16, large)-Net in Base 9 — Upper bound on s
There is no (61, 77, large)-net in base 9, because
- 14 times m-reduction [i] would yield (61, 63, large)-net in base 9, but