Best Known (81, 101, s)-Nets in Base 8
(81, 101, 3305)-Net over F8 — Constructive and digital
Digital (81, 101, 3305)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (66, 86, 3277)-net over F8, using
- net defined by OOA [i] based on linear OOA(886, 3277, F8, 20, 20) (dual of [(3277, 20), 65454, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(886, 32770, F8, 20) (dual of [32770, 32684, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(886, 32773, F8, 20) (dual of [32773, 32687, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- 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(881, 32768, F8, 19) (dual of [32768, 32687, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(886, 32773, F8, 20) (dual of [32773, 32687, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(886, 32770, F8, 20) (dual of [32770, 32684, 21]-code), using
- net defined by OOA [i] based on linear OOA(886, 3277, F8, 20, 20) (dual of [(3277, 20), 65454, 21]-NRT-code), using
- digital (5, 15, 28)-net over F8, using
(81, 101, 6555)-Net in Base 8 — Constructive
(81, 101, 6555)-net in base 8, using
- 81 times duplication [i] based on (80, 100, 6555)-net in base 8, using
- base change [i] based on digital (55, 75, 6555)-net over F16, using
- net defined by OOA [i] based on linear OOA(1675, 6555, F16, 20, 20) (dual of [(6555, 20), 131025, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(1675, 65550, F16, 20) (dual of [65550, 65475, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(1673, 65536, F16, 20) (dual of [65536, 65463, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- OA 10-folding and stacking [i] based on linear OA(1675, 65550, F16, 20) (dual of [65550, 65475, 21]-code), using
- net defined by OOA [i] based on linear OOA(1675, 6555, F16, 20, 20) (dual of [(6555, 20), 131025, 21]-NRT-code), using
- base change [i] based on digital (55, 75, 6555)-net over F16, using
(81, 101, 71583)-Net over F8 — Digital
Digital (81, 101, 71583)-net over F8, using
(81, 101, large)-Net in Base 8 — Upper bound on s
There is no (81, 101, large)-net in base 8, because
- 18 times m-reduction [i] would yield (81, 83, large)-net in base 8, but