Best Known (116−75, 116, s)-Nets in Base 4
(116−75, 116, 56)-Net over F4 — Constructive and digital
Digital (41, 116, 56)-net over F4, using
- t-expansion [i] based on digital (33, 116, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the 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) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(116−75, 116, 75)-Net over F4 — Digital
Digital (41, 116, 75)-net over F4, using
- t-expansion [i] based on digital (40, 116, 75)-net over F4, using
- net from sequence [i] based on digital (40, 74)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 40 and N(F) ≥ 75, using
- net from sequence [i] based on digital (40, 74)-sequence over F4, using
(116−75, 116, 299)-Net in Base 4 — Upper bound on s
There is no (41, 116, 300)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(4116, 300, S4, 75), but
- the linear programming bound shows that M ≥ 6464 797858 730510 075007 646352 191601 758254 767824 883094 669028 865893 281872 177308 057446 516693 897945 662891 433844 560362 554677 851191 622996 365656 035845 716401 200310 839612 578911 449308 695601 901308 093236 233816 011409 843058 184451 226488 153734 498366 399468 218499 348610 322268 160000 000000 / 703971 314392 227904 434212 687438 485737 129519 187316 060725 351259 006871 197254 498335 242876 003553 867954 285607 077562 883304 888089 357569 168487 807481 727288 225812 136097 878623 386748 108103 111971 251088 305096 083141 > 4116 [i]