Best Known (121, 121+30, s)-Nets in Base 8
(121, 121+30, 2212)-Net over F8 — Constructive and digital
Digital (121, 151, 2212)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 20, 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 (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 (5, 20, 28)-net over F8, using
(121, 121+30, 4369)-Net in Base 8 — Constructive
(121, 151, 4369)-net in base 8, using
- net defined by OOA [i] based on OOA(8151, 4369, S8, 30, 30), using
- OA 15-folding and stacking [i] based on OA(8151, 65535, S8, 30), using
- discarding factors based on OA(8151, 65540, S8, 30), using
- discarding parts of the base [i] based on linear OA(16113, 65540, F16, 30) (dual of [65540, 65427, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] 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]
- linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- discarding parts of the base [i] based on linear OA(16113, 65540, F16, 30) (dual of [65540, 65427, 31]-code), using
- discarding factors based on OA(8151, 65540, S8, 30), using
- OA 15-folding and stacking [i] based on OA(8151, 65535, S8, 30), using
(121, 121+30, 84022)-Net over F8 — Digital
Digital (121, 151, 84022)-net over F8, using
(121, 121+30, large)-Net in Base 8 — Upper bound on s
There is no (121, 151, large)-net in base 8, because
- 28 times m-reduction [i] would yield (121, 123, large)-net in base 8, but