Best Known (127−26, 127, s)-Nets in Base 8
(127−26, 127, 2545)-Net over F8 — Constructive and digital
Digital (101, 127, 2545)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (85, 111, 2521)-net over F8, using
- net defined by OOA [i] based on linear OOA(8111, 2521, F8, 26, 26) (dual of [(2521, 26), 65435, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8111, 32773, F8, 26) (dual of [32773, 32662, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- OA 13-folding and stacking [i] based on linear OA(8111, 32773, F8, 26) (dual of [32773, 32662, 27]-code), using
- net defined by OOA [i] based on linear OOA(8111, 2521, F8, 26, 26) (dual of [(2521, 26), 65435, 27]-NRT-code), using
- digital (3, 16, 24)-net over F8, using
(127−26, 127, 56276)-Net over F8 — Digital
Digital (101, 127, 56276)-net over F8, using
(127−26, 127, large)-Net in Base 8 — Upper bound on s
There is no (101, 127, large)-net in base 8, because
- 24 times m-reduction [i] would yield (101, 103, large)-net in base 8, but