Best Known (145, 183, s)-Nets in Base 4
(145, 183, 1056)-Net over F4 — Constructive and digital
Digital (145, 183, 1056)-net over F4, using
- 1 times m-reduction [i] based on digital (145, 184, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 46, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
- trace code for nets [i] based on digital (7, 46, 264)-net over F256, using
(145, 183, 4678)-Net over F4 — Digital
Digital (145, 183, 4678)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 4678, F4, 38) (dual of [4678, 4495, 39]-code), using
- 562 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 31 times 0, 1, 47 times 0, 1, 68 times 0, 1, 95 times 0, 1, 121 times 0, 1, 145 times 0) [i] based on linear OA(4169, 4102, F4, 38) (dual of [4102, 3933, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- 562 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 31 times 0, 1, 47 times 0, 1, 68 times 0, 1, 95 times 0, 1, 121 times 0, 1, 145 times 0) [i] based on linear OA(4169, 4102, F4, 38) (dual of [4102, 3933, 39]-code), using
(145, 183, 1662947)-Net in Base 4 — Upper bound on s
There is no (145, 183, 1662948)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 150 307280 082126 858286 748188 574530 137407 543039 573004 634338 825940 578418 265302 356068 135622 343612 474794 434431 698886 > 4183 [i]