MinT - Best Known (28, 93, s)-Nets in Base 4

Best Known (28, 93, s)-Nets in Base 4

(28, 93, 34)-Net over F₄ — Constructive and digital

Digital (28, 93, 34)-net over F₄, using

t-expansion [i] based on digital (21, 93, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(28, 93, 42)-Net in Base 4 — Constructive

(28, 93, 42)-net in base 4, using

t-expansion [i] based on (27, 93, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
  - base expansion [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(28, 93, 55)-Net over F₄ — Digital

Digital (28, 93, 55)-net over F₄, using

t-expansion [i] based on digital (26, 93, 55)-net over F₄, using
- net from sequence [i] based on digital (26, 54)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 26 and N(F) ≥ 55, using
    - Drinfeld modules of rank 1 [i]

(28, 93, 147)-Net in Base 4 — Upper bound on s

There is no (28, 93, 148)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁹³, 148, S₄, 65), but
- the linear programming bound shows that MÂ â‰¥ 31410 303083 703049 377310 817051 099884 117194 259592 068916 365914 768905 433278 533937 431277 207276 796100 647129 523955 480347 541504 / 271 727597 647736 395513 057790 697511 115852 689190 837400 656430 005393 > 4⁹³ [i]