MinT - Best Known (80, 134, s)-Nets in Base 2

Best Known (80, 134, s)-Nets in Base 2

(80, 134, 60)-Net over F₂ — Constructive and digital

Digital (80, 134, 60)-net over F₂, using

trace code for nets [i] based on digital (13, 67, 30)-net over F₄, using
- net from sequence [i] based on digital (13, 29)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(80, 134, 66)-Net over F₂ — Digital

Digital (80, 134, 66)-net over F₂, using

trace code for nets [i] based on digital (13, 67, 33)-net over F₄, using
- net from sequence [i] based on digital (13, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 33, using
    - Drinfeld modules of rank 1 [i]

(80, 134, 298)-Net in Base 2 — Upper bound on s

There is no (80, 134, 299)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2¹³⁴, 299, S₂, 54), but
- adding a parity check bit [i] would yield OA(2¹³⁵, 300, S₂, 55), but
  - the linear programming bound shows that MÂ â‰¥ 48 453210 492851 688423 719096 496218 730424 623843 475355 389039 083584 741794 713780 743579 191978 463824 301856 084801 540325 376000 / 597 625262 017249 457875 009714 443330 928540 125079 140107 131223 189140 092691 487281 > 2¹³⁵ [i]