Best Known (110, 146, s)-Nets in Base 4
(110, 146, 1028)-Net over F4 — Constructive and digital
Digital (110, 146, 1028)-net over F4, using
- 42 times duplication [i] based on digital (108, 144, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 36, 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, 36, 257)-net over F256, using
(110, 146, 1523)-Net over F4 — Digital
Digital (110, 146, 1523)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4146, 1523, F4, 36) (dual of [1523, 1377, 37]-code), using
- 1376 step Varšamov–Edel lengthening with (ri) = (10, 5, 3, 2, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 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, 0, 1, 0, 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, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 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, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0) [i] based on linear OA(436, 37, F4, 36) (dual of [37, 1, 37]-code or 37-arc in PG(35,4)), using
- dual of repetition code with length 37 [i]
- 1376 step Varšamov–Edel lengthening with (ri) = (10, 5, 3, 2, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 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, 0, 1, 0, 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, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 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, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0) [i] based on linear OA(436, 37, F4, 36) (dual of [37, 1, 37]-code or 37-arc in PG(35,4)), using
(110, 146, 192464)-Net in Base 4 — Upper bound on s
There is no (110, 146, 192465)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7957 235666 977815 662055 328674 255927 699419 134784 791044 598942 671102 228024 231098 464537 590640 > 4146 [i]