Best Known (84, 111, s)-Nets in Base 4
(84, 111, 1028)-Net over F4 — Constructive and digital
Digital (84, 111, 1028)-net over F4, using
- 1 times m-reduction [i] based on digital (84, 112, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 28, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 28, 257)-net over F256, using
(84, 111, 1321)-Net over F4 — Digital
Digital (84, 111, 1321)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4111, 1321, F4, 27) (dual of [1321, 1210, 28]-code), using
- 1209 step Varšamov–Edel lengthening with (ri) = (7, 4, 2, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 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, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 38 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 63 times 0, 1, 66 times 0) [i] based on linear OA(427, 28, F4, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,4)), using
- dual of repetition code with length 28 [i]
- 1209 step Varšamov–Edel lengthening with (ri) = (7, 4, 2, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 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, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 38 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 63 times 0, 1, 66 times 0) [i] based on linear OA(427, 28, F4, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,4)), using
(84, 111, 234757)-Net in Base 4 — Upper bound on s
There is no (84, 111, 234758)-net in base 4, because
- 1 times m-reduction [i] would yield (84, 110, 234758)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 685038 039410 336002 808290 280799 843013 811054 876164 201153 794968 074080 > 4110 [i]