Best Known (71, 71+20, s)-Nets in Base 9
(71, 71+20, 5907)-Net over F9 — Constructive and digital
Digital (71, 91, 5907)-net over F9, using
- net defined by OOA [i] based on linear OOA(991, 5907, F9, 20, 20) (dual of [(5907, 20), 118049, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(991, 59070, F9, 20) (dual of [59070, 58979, 21]-code), using
- construction XX applied to Ce(19) ⊂ Ce(15) ⊂ Ce(14) [i] based on
- linear OA(986, 59049, F9, 20) (dual of [59049, 58963, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(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(94, 20, F9, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,9)), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(19) ⊂ Ce(15) ⊂ Ce(14) [i] based on
- OA 10-folding and stacking [i] based on linear OA(991, 59070, F9, 20) (dual of [59070, 58979, 21]-code), using
(71, 71+20, 55741)-Net over F9 — Digital
Digital (71, 91, 55741)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(991, 55741, F9, 20) (dual of [55741, 55650, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(991, 59070, F9, 20) (dual of [59070, 58979, 21]-code), using
- construction XX applied to Ce(19) ⊂ Ce(15) ⊂ Ce(14) [i] based on
- linear OA(986, 59049, F9, 20) (dual of [59049, 58963, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(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(94, 20, F9, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,9)), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(19) ⊂ Ce(15) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(991, 59070, F9, 20) (dual of [59070, 58979, 21]-code), using
(71, 71+20, large)-Net in Base 9 — Upper bound on s
There is no (71, 91, large)-net in base 9, because
- 18 times m-reduction [i] would yield (71, 73, large)-net in base 9, but