Best Known (179−16, 179, s)-Nets in Base 3
(179−16, 179, 1048689)-Net over F3 — Constructive and digital
Digital (163, 179, 1048689)-net over F3, using
- 31 times duplication [i] based on digital (162, 178, 1048689)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (19, 27, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 9, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- trace code for nets [i] based on digital (1, 9, 38)-net over F27, using
- digital (135, 151, 1048575)-net over F3, using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- digital (19, 27, 114)-net over F3, using
- (u, u+v)-construction [i] based on
(179−16, 179, 4194506)-Net over F3 — Digital
Digital (163, 179, 4194506)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3179, 4194506, F3, 2, 16) (dual of [(4194506, 2), 8388833, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(328, 205, F3, 2, 8) (dual of [(205, 2), 382, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(328, 205, F3, 8) (dual of [205, 177, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(328, 251, F3, 8) (dual of [251, 223, 9]-code), using
- construction XX applied to Ce(7) ⊂ Ce(6) ⊂ Ce(4) [i] based on
- linear OA(326, 243, F3, 8) (dual of [243, 217, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(321, 243, F3, 7) (dual of [243, 222, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(316, 243, F3, 5) (dual of [243, 227, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(7) ⊂ Ce(6) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(328, 251, F3, 8) (dual of [251, 223, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(328, 205, F3, 8) (dual of [205, 177, 9]-code), using
- linear OOA(3151, 4194301, F3, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- linear OOA(328, 205, F3, 2, 8) (dual of [(205, 2), 382, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(179−16, 179, large)-Net in Base 3 — Upper bound on s
There is no (163, 179, large)-net in base 3, because
- 14 times m-reduction [i] would yield (163, 165, large)-net in base 3, but