Best Known (248−64, 248, s)-Nets in Base 4
(248−64, 248, 545)-Net over F4 — Constructive and digital
Digital (184, 248, 545)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 35, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (149, 213, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 71, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 71, 177)-net over F64, using
- digital (3, 35, 14)-net over F4, using
(248−64, 248, 648)-Net in Base 4 — Constructive
(184, 248, 648)-net in base 4, using
- t-expansion [i] based on (183, 248, 648)-net in base 4, using
- 1 times m-reduction [i] based on (183, 249, 648)-net in base 4, using
- trace code for nets [i] based on (17, 83, 216)-net in base 64, using
- 1 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
- base change [i] based on digital (5, 72, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 72, 216)-net over F128, using
- 1 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
- trace code for nets [i] based on (17, 83, 216)-net in base 64, using
- 1 times m-reduction [i] based on (183, 249, 648)-net in base 4, using
(248−64, 248, 1931)-Net over F4 — Digital
Digital (184, 248, 1931)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4248, 1931, F4, 64) (dual of [1931, 1683, 65]-code), using
- 1682 step Varšamov–Edel lengthening with (ri) = (18, 7, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 33 times 0, 1, 35 times 0, 1, 35 times 0, 1, 36 times 0, 1, 36 times 0, 1, 38 times 0, 1, 38 times 0, 1, 40 times 0) [i] based on linear OA(464, 65, F4, 64) (dual of [65, 1, 65]-code or 65-arc in PG(63,4)), using
- dual of repetition code with length 65 [i]
- 1682 step Varšamov–Edel lengthening with (ri) = (18, 7, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 33 times 0, 1, 35 times 0, 1, 35 times 0, 1, 36 times 0, 1, 36 times 0, 1, 38 times 0, 1, 38 times 0, 1, 40 times 0) [i] based on linear OA(464, 65, F4, 64) (dual of [65, 1, 65]-code or 65-arc in PG(63,4)), using
(248−64, 248, 197545)-Net in Base 4 — Upper bound on s
There is no (184, 248, 197546)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 204612 759164 602802 029720 855302 943448 579602 272197 195318 654882 618713 314440 669315 733553 659452 669067 326204 590703 905784 784277 000687 105546 683058 314201 534577 > 4248 [i]