Best Known (81, 81+20, s)-Nets in Base 9
(81, 81+20, 5937)-Net over F9 — Constructive and digital
Digital (81, 101, 5937)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (66, 86, 5905)-net over F9, using
- net defined by OOA [i] based on linear OOA(986, 5905, F9, 20, 20) (dual of [(5905, 20), 118014, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(986, 59050, F9, 20) (dual of [59050, 58964, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(986, 59054, F9, 20) (dual of [59054, 58968, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [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(981, 59049, F9, 19) (dual of [59049, 58968, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(986, 59054, F9, 20) (dual of [59054, 58968, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(986, 59050, F9, 20) (dual of [59050, 58964, 21]-code), using
- net defined by OOA [i] based on linear OOA(986, 5905, F9, 20, 20) (dual of [(5905, 20), 118014, 21]-NRT-code), using
- digital (5, 15, 32)-net over F9, using
(81, 81+20, 117142)-Net over F9 — Digital
Digital (81, 101, 117142)-net over F9, using
(81, 81+20, large)-Net in Base 9 — Upper bound on s
There is no (81, 101, large)-net in base 9, because
- 18 times m-reduction [i] would yield (81, 83, large)-net in base 9, but