Best Known (88−24, 88, s)-Nets in Base 4
(88−24, 88, 384)-Net over F4 — Constructive and digital
Digital (64, 88, 384)-net over F4, using
- 41 times duplication [i] based on digital (63, 87, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 29, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 29, 128)-net over F64, using
(88−24, 88, 387)-Net in Base 4 — Constructive
(64, 88, 387)-net in base 4, using
- 44 times duplication [i] based on (60, 84, 387)-net in base 4, using
- trace code for nets [i] based on (4, 28, 129)-net in base 64, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- trace code for nets [i] based on (4, 28, 129)-net in base 64, using
(88−24, 88, 644)-Net over F4 — Digital
Digital (64, 88, 644)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(488, 644, F4, 24) (dual of [644, 556, 25]-code), using
- 555 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 2, 1, 1, 1, 1, 1, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 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, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0) [i] based on linear OA(424, 25, F4, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,4)), using
- dual of repetition code with length 25 [i]
- 555 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 2, 1, 1, 1, 1, 1, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 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, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0) [i] based on linear OA(424, 25, F4, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,4)), using
(88−24, 88, 45841)-Net in Base 4 — Upper bound on s
There is no (64, 88, 45842)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 95798 912635 044106 431882 621121 114804 047209 052425 442220 > 488 [i]