MinT - Best Known (255−159, 255, s)-Nets in Base 4

Best Known (255−159, 255, s)-Nets in Base 4

(255−159, 255, 104)-Net over F₄ — Constructive and digital

Digital (96, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(255−159, 255, 144)-Net over F₄ — Digital

Digital (96, 255, 144)-net over F₄, using

t-expansion [i] based on digital (91, 255, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(255−159, 255, 805)-Net in Base 4 — Upper bound on s

There is no (96, 255, 806)-net in base 4, because

1 times m-reduction [i] would yield (96, 254, 806)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 880 021000 268414 335224 906217 180353 714948 339578 486606 225888 164657 968853 352363 276021 706188 926704 907114 322475 849433 166024 945882 261604 311091 089972 795381 909440 > 4²⁵⁴ [i]