Best Known (140−16, 140, s)-Nets in Base 9
(140−16, 140, 2097350)-Net over F9 — Constructive and digital
Digital (124, 140, 2097350)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (10, 18, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 9, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 9, 100)-net over F81, using
- digital (106, 122, 2097150)-net over F9, using
- net defined by OOA [i] based on linear OOA(9122, 2097150, F9, 18, 16) (dual of [(2097150, 18), 37748578, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(9122, 8388601, F9, 2, 16) (dual of [(8388601, 2), 16777080, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9122, 8388602, F9, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code), using
- trace code [i] based on linear OOA(8161, 4194301, F81, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8161, 8388602, F81, 16) (dual of [8388602, 8388541, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- OOA 2-folding [i] based on linear OA(8161, 8388602, F81, 16) (dual of [8388602, 8388541, 17]-code), using
- trace code [i] based on linear OOA(8161, 4194301, F81, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9122, 8388602, F9, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(9122, 8388601, F9, 2, 16) (dual of [(8388601, 2), 16777080, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(9122, 2097150, F9, 18, 16) (dual of [(2097150, 18), 37748578, 17]-NRT-code), using
- digital (10, 18, 200)-net over F9, using
(140−16, 140, large)-Net over F9 — Digital
Digital (124, 140, large)-net over F9, using
- 5 times m-reduction [i] based on digital (124, 145, large)-net over F9, using
(140−16, 140, large)-Net in Base 9 — Upper bound on s
There is no (124, 140, large)-net in base 9, because
- 14 times m-reduction [i] would yield (124, 126, large)-net in base 9, but