Best Known (24, 79, s)-Nets in Base 4
(24, 79, 34)-Net over F4 — Constructive and digital
Digital (24, 79, 34)-net over F4, using
- t-expansion [i] based on digital (21, 79, 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, 79, 35)-Net in Base 4 — Constructive
(24, 79, 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, 79, 49)-Net over F4 — Digital
Digital (24, 79, 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, 79, 142)-Net in Base 4 — Upper bound on s
There is no (24, 79, 143)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(479, 143, S4, 55), but
- the linear programming bound shows that M ≥ 28259 050341 636931 864361 560961 126150 779700 072182 758448 850273 250995 545713 854838 785276 137401 021079 495403 638500 666063 356680 186698 534971 563795 093767 473603 933759 522314 524416 452239 294464 / 73597 952581 605396 851220 297809 584605 839998 910652 655161 071676 907986 565444 588487 008569 321443 767449 410699 101937 740852 888900 463488 574375 > 479 [i]