Best Known (162, 162+45, s)-Nets in Base 4
(162, 162+45, 1052)-Net over F4 — Constructive and digital
Digital (162, 207, 1052)-net over F4, using
- 1 times m-reduction [i] based on digital (162, 208, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 52, 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, 52, 263)-net over F256, using
(162, 162+45, 4172)-Net over F4 — Digital
Digital (162, 207, 4172)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4207, 4172, F4, 45) (dual of [4172, 3965, 46]-code), using
- 68 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 17 times 0, 1, 29 times 0) [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- 68 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 17 times 0, 1, 29 times 0) [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
(162, 162+45, 1309774)-Net in Base 4 — Upper bound on s
There is no (162, 207, 1309775)-net in base 4, because
- 1 times m-reduction [i] would yield (162, 206, 1309775)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10576 900688 653107 543118 764601 971701 915601 862528 349471 281785 355495 878358 423545 970090 670562 569743 286222 915443 510119 708081 801196 > 4206 [i]