Best Known (206, 206+44, s)-Nets in Base 3
(206, 206+44, 1480)-Net over F3 — Constructive and digital
Digital (206, 250, 1480)-net over F3, using
- 32 times duplication [i] based on digital (204, 248, 1480)-net over F3, using
- t-expansion [i] based on digital (202, 248, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 62, 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, 62, 370)-net over F81, using
- t-expansion [i] based on digital (202, 248, 1480)-net over F3, using
(206, 206+44, 5524)-Net over F3 — Digital
Digital (206, 250, 5524)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3250, 5524, F3, 44) (dual of [5524, 5274, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3250, 6618, F3, 44) (dual of [6618, 6368, 45]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3248, 6616, F3, 44) (dual of [6616, 6368, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(36) [i] based on
- linear OA(3233, 6561, F3, 44) (dual of [6561, 6328, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(43) ⊂ Ce(36) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3248, 6616, F3, 44) (dual of [6616, 6368, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3250, 6618, F3, 44) (dual of [6618, 6368, 45]-code), using
(206, 206+44, 1195770)-Net in Base 3 — Upper bound on s
There is no (206, 250, 1195771)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 190687 166448 172552 531996 227742 233344 897493 799426 393499 891757 446994 079144 251948 901850 617825 995389 776267 416710 516843 026989 > 3250 [i]