Best Known (89−59, 89, s)-Nets in Base 4
(89−59, 89, 34)-Net over F4 — Constructive and digital
Digital (30, 89, 34)-net over F4, using
- t-expansion [i] based on digital (21, 89, 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
(89−59, 89, 43)-Net in Base 4 — Constructive
(30, 89, 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
(89−59, 89, 55)-Net over F4 — Digital
Digital (30, 89, 55)-net over F4, using
- t-expansion [i] based on digital (26, 89, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
(89−59, 89, 238)-Net in Base 4 — Upper bound on s
There is no (30, 89, 239)-net in base 4, because
- 1 times m-reduction [i] would yield (30, 88, 239)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 103505 876700 510117 111600 381574 763828 265051 894560 182084 > 488 [i]