MinT - Best Known (106, 255, s)-Nets in Base 4

Best Known (106, 255, s)-Nets in Base 4

(106, 255, 130)-Net over F₄ — Constructive and digital

Digital (106, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(106, 255, 144)-Net over F₄ — Digital

Digital (106, 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]

(106, 255, 1042)-Net in Base 4 — Upper bound on s

There is no (106, 255, 1043)-net in base 4, because

1 times m-reduction [i] would yield (106, 254, 1043)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 861 697629 477327 753117 656347 712393 836146 527794 684395 197879 660331 198938 333567 248020 241235 033162 006111 361225 767811 136177 827667 546070 774892 809177 522644 049440 > 4²⁵⁴ [i]