Best Known (123, 153, s)-Nets in Base 8
(123, 153, 2218)-Net over F8 — Constructive and digital
Digital (123, 153, 2218)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 22, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (101, 131, 2184)-net over F8, using
- net defined by OOA [i] based on linear OOA(8131, 2184, F8, 30, 30) (dual of [(2184, 30), 65389, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
- net defined by OOA [i] based on linear OOA(8131, 2184, F8, 30, 30) (dual of [(2184, 30), 65389, 31]-NRT-code), using
- digital (7, 22, 34)-net over F8, using
(123, 153, 4369)-Net in Base 8 — Constructive
(123, 153, 4369)-net in base 8, using
- 81 times duplication [i] based on (122, 152, 4369)-net in base 8, using
- base change [i] based on digital (84, 114, 4369)-net over F16, using
- 161 times duplication [i] based on digital (83, 113, 4369)-net over F16, using
- net defined by OOA [i] based on linear OOA(16113, 4369, F16, 30, 30) (dual of [(4369, 30), 130957, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(16113, 65535, F16, 30) (dual of [65535, 65422, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(16113, 65536, F16, 30) (dual of [65536, 65423, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(16113, 65536, F16, 30) (dual of [65536, 65423, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(16113, 65535, F16, 30) (dual of [65535, 65422, 31]-code), using
- net defined by OOA [i] based on linear OOA(16113, 4369, F16, 30, 30) (dual of [(4369, 30), 130957, 31]-NRT-code), using
- 161 times duplication [i] based on digital (83, 113, 4369)-net over F16, using
- base change [i] based on digital (84, 114, 4369)-net over F16, using
(123, 153, 96976)-Net over F8 — Digital
Digital (123, 153, 96976)-net over F8, using
(123, 153, large)-Net in Base 8 — Upper bound on s
There is no (123, 153, large)-net in base 8, because
- 28 times m-reduction [i] would yield (123, 125, large)-net in base 8, but