Best Known (166−32, 166, s)-Nets in Base 8
(166−32, 166, 2094)-Net over F8 — Constructive and digital
Digital (134, 166, 2094)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 26, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (108, 140, 2048)-net over F8, using
- net defined by OOA [i] based on linear OOA(8140, 2048, F8, 32, 32) (dual of [(2048, 32), 65396, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(8140, 32768, F8, 32) (dual of [32768, 32628, 33]-code), using
- 1 times truncation [i] based on linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using
- OA 16-folding and stacking [i] based on linear OA(8140, 32768, F8, 32) (dual of [32768, 32628, 33]-code), using
- net defined by OOA [i] based on linear OOA(8140, 2048, F8, 32, 32) (dual of [(2048, 32), 65396, 33]-NRT-code), using
- digital (10, 26, 46)-net over F8, using
(166−32, 166, 4097)-Net in Base 8 — Constructive
(134, 166, 4097)-net in base 8, using
- net defined by OOA [i] based on OOA(8166, 4097, S8, 32, 32), using
- OA 16-folding and stacking [i] based on OA(8166, 65552, S8, 32), using
- discarding factors based on OA(8166, 65554, S8, 32), using
- discarding parts of the base [i] based on linear OA(16124, 65554, F16, 32) (dual of [65554, 65430, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
- linear OA(16121, 65536, F16, 33) (dual of [65536, 65415, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
- discarding parts of the base [i] based on linear OA(16124, 65554, F16, 32) (dual of [65554, 65430, 33]-code), using
- discarding factors based on OA(8166, 65554, S8, 32), using
- OA 16-folding and stacking [i] based on OA(8166, 65552, S8, 32), using
(166−32, 166, 121588)-Net over F8 — Digital
Digital (134, 166, 121588)-net over F8, using
(166−32, 166, large)-Net in Base 8 — Upper bound on s
There is no (134, 166, large)-net in base 8, because
- 30 times m-reduction [i] would yield (134, 136, large)-net in base 8, but