Best Known (134, 157, s)-Nets in Base 8
(134, 157, 190678)-Net over F8 — Constructive and digital
Digital (134, 157, 190678)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 16, 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 (118, 141, 190650)-net over F8, using
- net defined by OOA [i] based on linear OOA(8141, 190650, F8, 23, 23) (dual of [(190650, 23), 4384809, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8141, 2097151, F8, 23) (dual of [2097151, 2097010, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8141, 2097151, F8, 23) (dual of [2097151, 2097010, 24]-code), using
- net defined by OOA [i] based on linear OOA(8141, 190650, F8, 23, 23) (dual of [(190650, 23), 4384809, 24]-NRT-code), using
- digital (5, 16, 28)-net over F8, using
(134, 157, 3601926)-Net over F8 — Digital
Digital (134, 157, 3601926)-net over F8, using
(134, 157, large)-Net in Base 8 — Upper bound on s
There is no (134, 157, large)-net in base 8, because
- 21 times m-reduction [i] would yield (134, 136, large)-net in base 8, but