MinT - Best Known (155, 155+∞, s)-Nets in Base 2

Best Known (155, 155+∞, s)-Nets in Base 2

Digital (155, m, 58)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (155, 57)-sequence over F₂, using
- base reduction for sequences [i] based on digital (49, 57)-sequence over F₄, using
  - s-reduction based on digital (49, 65)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
      - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Digital (155, m, 81)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (155, 80)-sequence over F₂, using
- t-expansion [i] based on digital (126, 80)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 126 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

There is no (155, m, 166)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (155, 1318, 166)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹³¹⁸, 166, S₂, 8, 1163), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1979 750147 160820 289832 578668 204454 671431 870384 838654 852463 609023 808215 475171 569693 074692 383314 780667 667065 430003 264289 537233 677854 646521 475457 680883 213049 263303 510185 976953 383261 649596 791097 468138 382388 618400 460676 774004 830345 131011 151394 955950 451167 271365 983500 163549 140427 763003 244150 535381 589052 043463 205162 648718 566267 363906 081619 757049 036689 236583 933245 759317 044514 464419 452826 540925 950911 053824 / 291 > 2¹³¹⁸ [i]