Best Known (156, 179, s)-Nets in Base 3
(156, 179, 16113)-Net over F3 — Constructive and digital
Digital (156, 179, 16113)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- digital (143, 166, 16105)-net over F3, using
- net defined by OOA [i] based on linear OOA(3166, 16105, F3, 23, 23) (dual of [(16105, 23), 370249, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3166, 177156, F3, 23) (dual of [177156, 176990, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, 177158, F3, 23) (dual of [177158, 176992, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3166, 177158, F3, 23) (dual of [177158, 176992, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3166, 177156, F3, 23) (dual of [177156, 176990, 24]-code), using
- net defined by OOA [i] based on linear OOA(3166, 16105, F3, 23, 23) (dual of [(16105, 23), 370249, 24]-NRT-code), using
- digital (2, 13, 8)-net over F3, using
(156, 179, 69292)-Net over F3 — Digital
Digital (156, 179, 69292)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3179, 69292, F3, 2, 23) (dual of [(69292, 2), 138405, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3179, 88602, F3, 2, 23) (dual of [(88602, 2), 177025, 24]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3177, 88601, F3, 2, 23) (dual of [(88601, 2), 177025, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3177, 177202, F3, 23) (dual of [177202, 177025, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(311, 55, F3, 5) (dual of [55, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(3177, 177202, F3, 23) (dual of [177202, 177025, 24]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3177, 88601, F3, 2, 23) (dual of [(88601, 2), 177025, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3179, 88602, F3, 2, 23) (dual of [(88602, 2), 177025, 24]-NRT-code), using
(156, 179, large)-Net in Base 3 — Upper bound on s
There is no (156, 179, large)-net in base 3, because
- 21 times m-reduction [i] would yield (156, 158, large)-net in base 3, but