Best Known (236−38, 236, s)-Nets in Base 3
(236−38, 236, 1487)-Net over F3 — Constructive and digital
Digital (198, 236, 1487)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 20, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (178, 216, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 54, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 54, 370)-net over F81, using
- digital (1, 20, 7)-net over F3, using
(236−38, 236, 9861)-Net over F3 — Digital
Digital (198, 236, 9861)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3236, 9861, F3, 2, 38) (dual of [(9861, 2), 19486, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3236, 19722, F3, 38) (dual of [19722, 19486, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(31) [i] based on
- linear OA(3226, 19683, F3, 38) (dual of [19683, 19457, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), using
- construction X applied to Ce(37) ⊂ Ce(31) [i] based on
- OOA 2-folding [i] based on linear OA(3236, 19722, F3, 38) (dual of [19722, 19486, 39]-code), using
(236−38, 236, 3346041)-Net in Base 3 — Upper bound on s
There is no (198, 236, 3346042)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 39867 342790 457752 716230 459844 539080 216154 012003 497363 454985 553952 642010 353145 122475 254668 724400 204812 213748 612945 > 3236 [i]