MinT - Best Known (250−148, 250, s)-Nets in Base 4

Best Known (250−148, 250, s)-Nets in Base 4

(250−148, 250, 104)-Net over F₄ — Constructive and digital

Digital (102, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 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]

(250−148, 250, 144)-Net over F₄ — Digital

Digital (102, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 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]

(250−148, 250, 963)-Net in Base 4 — Upper bound on s

There is no (102, 250, 964)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 497852 272342 265159 481003 737256 435179 210732 453367 526781 065597 828754 808776 046354 465535 914918 737654 040187 368576 593969 170048 098459 343588 773849 768418 292560 > 4²⁵⁰ [i]