Best Known (87, 108, s)-Nets in Base 9
(87, 108, 5941)-Net over F9 — Constructive and digital
Digital (87, 108, 5941)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 17, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- digital (70, 91, 5905)-net over F9, using
- net defined by OOA [i] based on linear OOA(991, 5905, F9, 21, 21) (dual of [(5905, 21), 123914, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(991, 59051, F9, 21) (dual of [59051, 58960, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(991, 59054, F9, 21) (dual of [59054, 58963, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [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(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(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(20) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(991, 59054, F9, 21) (dual of [59054, 58963, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(991, 59051, F9, 21) (dual of [59051, 58960, 22]-code), using
- net defined by OOA [i] based on linear OOA(991, 5905, F9, 21, 21) (dual of [(5905, 21), 123914, 22]-NRT-code), using
- digital (7, 17, 36)-net over F9, using
(87, 108, 5943)-Net in Base 9 — Constructive
(87, 108, 5943)-net in base 9, using
- (u, u+v)-construction [i] based on
- (7, 17, 38)-net in base 9, using
- 1 times m-reduction [i] based on (7, 18, 38)-net in base 9, using
- base change [i] based on digital (1, 12, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- base change [i] based on digital (1, 12, 38)-net over F27, using
- 1 times m-reduction [i] based on (7, 18, 38)-net in base 9, using
- digital (70, 91, 5905)-net over F9, using
- net defined by OOA [i] based on linear OOA(991, 5905, F9, 21, 21) (dual of [(5905, 21), 123914, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(991, 59051, F9, 21) (dual of [59051, 58960, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(991, 59054, F9, 21) (dual of [59054, 58963, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [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(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(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(20) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(991, 59054, F9, 21) (dual of [59054, 58963, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(991, 59051, F9, 21) (dual of [59051, 58960, 22]-code), using
- net defined by OOA [i] based on linear OOA(991, 5905, F9, 21, 21) (dual of [(5905, 21), 123914, 22]-NRT-code), using
- (7, 17, 38)-net in base 9, using
(87, 108, 147623)-Net over F9 — Digital
Digital (87, 108, 147623)-net over F9, using
(87, 108, large)-Net in Base 9 — Upper bound on s
There is no (87, 108, large)-net in base 9, because
- 19 times m-reduction [i] would yield (87, 89, large)-net in base 9, but