Best Known (24, 24+54, s)-Nets in Base 4
(24, 24+54, 34)-Net over F4 — Constructive and digital
Digital (24, 78, 34)-net over F4, using
- t-expansion [i] based on digital (21, 78, 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
(24, 24+54, 35)-Net in Base 4 — Constructive
(24, 78, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
(24, 24+54, 49)-Net over F4 — Digital
Digital (24, 78, 49)-net over F4, using
- net from sequence [i] based on digital (24, 48)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 24 and N(F) ≥ 49, using
(24, 24+54, 148)-Net in Base 4 — Upper bound on s
There is no (24, 78, 149)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(478, 149, S4, 54), but
- the linear programming bound shows that M ≥ 859638 874001 066114 473096 016512 705998 294269 037467 429953 824525 218785 286235 420689 797732 422528 806123 657652 370340 209627 009813 504992 246349 565273 026462 351977 172225 385800 078260 779135 484536 194539 933522 635484 632068 348452 995283 393354 678600 334492 176219 129774 081398 386032 994252 648859 303936 / 8 997897 330004 828509 038062 052921 938018 348257 243821 445922 633930 476682 832052 409899 229482 045351 319965 341067 624457 763251 426292 962578 918246 464446 537140 256730 858305 555295 472405 031903 270188 955856 053422 543586 226694 923453 684150 192241 123125 > 478 [i]