Best Known (105, 105+50, s)-Nets in Base 8
(105, 105+50, 513)-Net over F8 — Constructive and digital
Digital (105, 155, 513)-net over F8, using
- base reduction for projective spaces (embedding PG(77,64) in PG(154,8)) for nets [i] based on digital (28, 78, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(105, 105+50, 576)-Net in Base 8 — Constructive
(105, 155, 576)-net in base 8, using
- 13 times m-reduction [i] based on (105, 168, 576)-net in base 8, using
- trace code for nets [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
- trace code for nets [i] based on (21, 84, 288)-net in base 64, using
(105, 105+50, 1988)-Net over F8 — Digital
Digital (105, 155, 1988)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8155, 1988, F8, 50) (dual of [1988, 1833, 51]-code), using
- 1832 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 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, 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, 7 times 0, 1, 7 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, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 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, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 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, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 64 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 76 times 0, 1, 80 times 0) [i] based on linear OA(850, 51, F8, 50) (dual of [51, 1, 51]-code or 51-arc in PG(49,8)), using
- dual of repetition code with length 51 [i]
- 1832 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 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, 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, 7 times 0, 1, 7 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, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 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, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 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, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 64 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 76 times 0, 1, 80 times 0) [i] based on linear OA(850, 51, F8, 50) (dual of [51, 1, 51]-code or 51-arc in PG(49,8)), using
(105, 105+50, 577662)-Net in Base 8 — Upper bound on s
There is no (105, 155, 577663)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 95 271229 304289 721017 188886 019160 252556 276645 742010 361707 263389 777344 644280 018481 774852 572191 714379 615809 465901 297999 179162 966666 731618 373250 > 8155 [i]