Best Known (84, 84+21, s)-Nets in Base 8
(84, 84+21, 3302)-Net over F8 — Constructive and digital
Digital (84, 105, 3302)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- digital (70, 91, 3277)-net over F8, using
- net defined by OOA [i] based on linear OOA(891, 3277, F8, 21, 21) (dual of [(3277, 21), 68726, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(891, 32771, F8, 21) (dual of [32771, 32680, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(891, 32773, F8, 21) (dual of [32773, 32682, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(891, 32768, F8, 21) (dual of [32768, 32677, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 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(891, 32773, F8, 21) (dual of [32773, 32682, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(891, 32771, F8, 21) (dual of [32771, 32680, 22]-code), using
- net defined by OOA [i] based on linear OOA(891, 3277, F8, 21, 21) (dual of [(3277, 21), 68726, 22]-NRT-code), using
- digital (4, 14, 25)-net over F8, using
(84, 84+21, 6554)-Net in Base 8 — Constructive
(84, 105, 6554)-net in base 8, using
- 81 times duplication [i] based on (83, 104, 6554)-net in base 8, using
- base change [i] based on digital (57, 78, 6554)-net over F16, using
- net defined by OOA [i] based on linear OOA(1678, 6554, F16, 21, 21) (dual of [(6554, 21), 137556, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1678, 65541, F16, 21) (dual of [65541, 65463, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1678, 65545, F16, 21) (dual of [65545, 65467, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(1677, 65536, F16, 21) (dual of [65536, 65459, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(161, 9, F16, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(1678, 65545, F16, 21) (dual of [65545, 65467, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1678, 65541, F16, 21) (dual of [65541, 65463, 22]-code), using
- net defined by OOA [i] based on linear OOA(1678, 6554, F16, 21, 21) (dual of [(6554, 21), 137556, 22]-NRT-code), using
- base change [i] based on digital (57, 78, 6554)-net over F16, using
(84, 84+21, 65388)-Net over F8 — Digital
Digital (84, 105, 65388)-net over F8, using
(84, 84+21, large)-Net in Base 8 — Upper bound on s
There is no (84, 105, large)-net in base 8, because
- 19 times m-reduction [i] would yield (84, 86, large)-net in base 8, but