Best Known (183−34, 183, s)-Nets in Base 3
(183−34, 183, 696)-Net over F3 — Constructive and digital
Digital (149, 183, 696)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 19, 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 (130, 164, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 41, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 41, 172)-net over F81, using
- digital (2, 19, 8)-net over F3, using
(183−34, 183, 3292)-Net over F3 — Digital
Digital (149, 183, 3292)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3183, 3292, F3, 2, 34) (dual of [(3292, 2), 6401, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3183, 6584, F3, 34) (dual of [6584, 6401, 35]-code), using
- construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3153, 6561, F3, 29) (dual of [6561, 6408, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(34, 21, F3, 2) (dual of [21, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), 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(33) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- OOA 2-folding [i] based on linear OA(3183, 6584, F3, 34) (dual of [6584, 6401, 35]-code), using
(183−34, 183, 490874)-Net in Base 3 — Upper bound on s
There is no (149, 183, 490875)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2056 814448 703713 278134 353509 800444 292615 197655 922914 829861 484904 270146 711010 830883 192151 > 3183 [i]