Best Known (113−82, 113, s)-Nets in Base 4
(113−82, 113, 34)-Net over F4 — Constructive and digital
Digital (31, 113, 34)-net over F4, using
- t-expansion [i] based on digital (21, 113, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(113−82, 113, 43)-Net in Base 4 — Constructive
(31, 113, 43)-net in base 4, using
- t-expansion [i] based on (30, 113, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
(113−82, 113, 60)-Net over F4 — Digital
Digital (31, 113, 60)-net over F4, using
- net from sequence [i] based on digital (31, 59)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 31 and N(F) ≥ 60, using
(113−82, 113, 131)-Net in Base 4 — Upper bound on s
There is no (31, 113, 132)-net in base 4, because
- 1 times m-reduction [i] would yield (31, 112, 132)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(4112, 132, S4, 81), but
- the linear programming bound shows that M ≥ 11778 504777 779688 498524 359999 043750 103927 634385 012592 570847 246118 930944 386301 689856 / 405 533359 108881 > 4112 [i]
- extracting embedded orthogonal array [i] would yield OA(4112, 132, S4, 81), but