Best Known (191−41, 191, s)-Nets in Base 4
(191−41, 191, 1052)-Net over F4 — Constructive and digital
Digital (150, 191, 1052)-net over F4, using
- 1 times m-reduction [i] based on digital (150, 192, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
(191−41, 191, 4207)-Net over F4 — Digital
Digital (150, 191, 4207)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4191, 4207, F4, 41) (dual of [4207, 4016, 42]-code), using
- 100 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0, 1, 37 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- 100 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0, 1, 37 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
(191−41, 191, 1451276)-Net in Base 4 — Upper bound on s
There is no (150, 191, 1451277)-net in base 4, because
- 1 times m-reduction [i] would yield (150, 190, 1451277)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 462654 494128 519304 881115 405492 458243 489575 463914 438266 086228 144919 318637 998408 095107 327190 474628 811839 227699 413296 > 4190 [i]