Best Known (133, 133+28, s)-Nets in Base 8
(133, 133+28, 18742)-Net over F8 — Constructive and digital
Digital (133, 161, 18742)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (117, 145, 18725)-net over F8, using
- net defined by OOA [i] based on linear OOA(8145, 18725, F8, 28, 28) (dual of [(18725, 28), 524155, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8145, 262150, F8, 28) (dual of [262150, 262005, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(80, 6, F8, 0) (dual of [6, 6, 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(27) ⊂ Ce(26) [i] based on
- OA 14-folding and stacking [i] based on linear OA(8145, 262150, F8, 28) (dual of [262150, 262005, 29]-code), using
- net defined by OOA [i] based on linear OOA(8145, 18725, F8, 28, 28) (dual of [(18725, 28), 524155, 29]-NRT-code), using
- digital (2, 16, 17)-net over F8, using
(133, 133+28, 378805)-Net over F8 — Digital
Digital (133, 161, 378805)-net over F8, using
(133, 133+28, large)-Net in Base 8 — Upper bound on s
There is no (133, 161, large)-net in base 8, because
- 26 times m-reduction [i] would yield (133, 135, large)-net in base 8, but