Best Known (103−37, 103, s)-Nets in Base 8
(103−37, 103, 354)-Net over F8 — Constructive and digital
Digital (66, 103, 354)-net over F8, using
- 15 times m-reduction [i] based on digital (66, 118, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 59, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 59, 177)-net over F64, using
(103−37, 103, 516)-Net in Base 8 — Constructive
(66, 103, 516)-net in base 8, using
- 1 times m-reduction [i] based on (66, 104, 516)-net in base 8, using
- base change [i] based on digital (40, 78, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 39, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 39, 258)-net over F256, using
- base change [i] based on digital (40, 78, 516)-net over F16, using
(103−37, 103, 801)-Net over F8 — Digital
Digital (66, 103, 801)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8103, 801, F8, 37) (dual of [801, 698, 38]-code), using
- 697 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 0, 1, 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, 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, 6 times 0, 1, 6 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, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0) [i] based on linear OA(837, 38, F8, 37) (dual of [38, 1, 38]-code or 38-arc in PG(36,8)), using
- dual of repetition code with length 38 [i]
- 697 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 0, 1, 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, 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, 6 times 0, 1, 6 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, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0) [i] based on linear OA(837, 38, F8, 37) (dual of [38, 1, 38]-code or 38-arc in PG(36,8)), using
(103−37, 103, 141419)-Net in Base 8 — Upper bound on s
There is no (66, 103, 141420)-net in base 8, because
- 1 times m-reduction [i] would yield (66, 102, 141420)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 130 385906 532672 934453 199205 487841 870182 971442 952153 388839 361433 026869 903062 434246 382070 623930 > 8102 [i]