Best Known (118, 118+51, s)-Nets in Base 8
(118, 118+51, 1026)-Net over F8 — Constructive and digital
Digital (118, 169, 1026)-net over F8, using
- t-expansion [i] based on digital (114, 169, 1026)-net over F8, using
- 3 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 86, 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
- trace code for nets [i] based on digital (28, 86, 513)-net over F64, using
- 3 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
(118, 118+51, 3166)-Net over F8 — Digital
Digital (118, 169, 3166)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8169, 3166, F8, 51) (dual of [3166, 2997, 52]-code), using
- 2996 step Varšamov–Edel lengthening with (ri) = (8, 4, 2, 1, 2, 1, 1, 1, 1, 1, 0, 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, 1, 0, 0, 0, 1, 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, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 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, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 48 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 69 times 0, 1, 73 times 0, 1, 76 times 0, 1, 79 times 0, 1, 82 times 0, 1, 86 times 0, 1, 90 times 0, 1, 93 times 0, 1, 98 times 0, 1, 102 times 0, 1, 106 times 0, 1, 111 times 0, 1, 116 times 0, 1, 121 times 0, 1, 126 times 0) [i] based on linear OA(851, 52, F8, 51) (dual of [52, 1, 52]-code or 52-arc in PG(50,8)), using
- dual of repetition code with length 52 [i]
- 2996 step Varšamov–Edel lengthening with (ri) = (8, 4, 2, 1, 2, 1, 1, 1, 1, 1, 0, 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, 1, 0, 0, 0, 1, 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, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 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, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 48 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 69 times 0, 1, 73 times 0, 1, 76 times 0, 1, 79 times 0, 1, 82 times 0, 1, 86 times 0, 1, 90 times 0, 1, 93 times 0, 1, 98 times 0, 1, 102 times 0, 1, 106 times 0, 1, 111 times 0, 1, 116 times 0, 1, 121 times 0, 1, 126 times 0) [i] based on linear OA(851, 52, F8, 51) (dual of [52, 1, 52]-code or 52-arc in PG(50,8)), using
(118, 118+51, 1703289)-Net in Base 8 — Upper bound on s
There is no (118, 169, 1703290)-net in base 8, because
- 1 times m-reduction [i] would yield (118, 168, 1703290)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 52 374452 449750 553669 224439 708779 724806 823794 457579 278967 868697 630618 756683 062175 668310 684149 003210 965380 722956 287470 551839 991793 310542 003963 704317 689425 > 8168 [i]