Best Known (201, 201+47, s)-Nets in Base 3
(201, 201+47, 896)-Net over F3 — Constructive and digital
Digital (201, 248, 896)-net over F3, using
- t-expansion [i] based on digital (199, 248, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 62, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 62, 224)-net over F81, using
(201, 201+47, 3400)-Net over F3 — Digital
Digital (201, 248, 3400)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3248, 3400, F3, 47) (dual of [3400, 3152, 48]-code), using
- 108 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0, 1, 34 times 0, 1, 55 times 0) [i] based on linear OA(3245, 3289, F3, 47) (dual of [3289, 3044, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(45) [i] based on
- linear OA(3245, 3281, F3, 47) (dual of [3281, 3036, 48]-code), using an extension Ce(46) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3237, 3281, F3, 46) (dual of [3281, 3044, 47]-code), using an extension Ce(45) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 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(46) ⊂ Ce(45) [i] based on
- 108 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0, 1, 34 times 0, 1, 55 times 0) [i] based on linear OA(3245, 3289, F3, 47) (dual of [3289, 3044, 48]-code), using
(201, 201+47, 627015)-Net in Base 3 — Upper bound on s
There is no (201, 248, 627016)-net in base 3, because
- 1 times m-reduction [i] would yield (201, 247, 627016)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7062 561334 139139 290855 004681 081006 662503 257052 882185 131315 747051 906163 014303 087583 687393 484589 388868 283152 524695 873121 > 3247 [i]